Not quite sure how you're getting such a low GWP as my calculations yield a GWP of 380 for Htourlao for example.
The problem is Htourlao is the only world with significant GWP and budget that reached 3 digits (my calculations showed 148 RU, with 1 RU = 3.8k local MCr value). Syoakh for example in my calculations had a budget of 18 RU. That creates problems if using T4 stats of military maintenance which are 3 RU per Size (+2 RU per Size per parsec between maintaining world and the unit). We know from the Mongoose Glorious Empire that there sits presumably the equivalent of a BatRon above Syoakh with J3 capability. A minimal T4 space unit with J3 would be A1D1J6, which is Size 8. That is 24 RU to maintain, but Syoakh is also described as maintaining ground forces and deep site meson guns. Therefore I assumed that ate up Syoakh's budget. If the Size 8 fleet were maintained from Htourlao that is 40 RU. Doable, but eats up much of Htourlao's budget. We know again from the Mongoose Glorious Empire that Htourlao maintains significant fleet assets as there is a carrier and battleship described as well. Let's assume it is another Size 8 fleet. That is another 24 RU in maintenance. So 66 RU eaten up. Yero'ilra is described having at least destroyers and pocket warships with Jump 3. Yero'ilra's local budget is < 2 RU so it cannot support any significant fleet assets. It is 5 hexes from Htourlao so every Size costs 13 RU. Even a minimal unit of Size 4 (A1J3) would cost 52 RU. That leaves 32 free budget for Htourlao.
However it gets worse. There are stranded no longer Jump capable battleships in Oihu (3 parsecs from Htourlao) and Keawoaw (2 parsecs away). Again for the sake of argument, assume a minimal A1D1 for battleships. That is a maintenance cost of 18 RU and 14 RU. So 0 RU left for Htourlao.
If Htourlao had a higher discretionary tax rate, it could still have a budget. At a total nearly confiscatory tax rate of 71% it would have 2 RU budget left, but an increasingly discontent population (my spreadsheet included Popularity calculations). But this does not count any Htourlao local garrison forces! These calculations all used pretty much the minimal strengths for military units and all other worlds are left undefended. Such a Glorious Empire has all the staying power of wet paper. Now maybe if Htourlao had capable administrators they could reduce waste and scrape a few more RU but in T4 that requires good Admin rolls year after year.
Such a finely balanced budget also renders it impossible for the Glorious Empire to conduct offensive operations as that would make maintenance costs skyrocket the further forces move from Htourlao.
While that still has them at a shortfall, it does explain their inability to mount ihatei operations, or offensives as you’ve described them. Have you considered their black market income and mercenary operations? The former could be a relatively high source of income while the latter might be not be of great value, but it might introduce a trade route into the Dustbelt, from which additional income might flow.
The impression given in the Glorious Empire book is that the black market is mostly the Glorious Empire importing critical technical parts and luxury goods. It does not seem like the Glorious Empire is exporting much. Mercenary operations again do not seem to be of a scale sufficient to make a significant dent at the scale of we are talking about here.
My calculations for Htourlao showed 1 Htourlao RU = ~3982 MCr. What are the typical operational overheads and profits of a typical Glorious Empire mercenary outfit? The old FASA books had an Aslan mercenary regiment with about 3300 individuals. I cannot imagine the Dustbelt having mass amounts of Credits to pay based on a quick look at their UWP (it would be too much work for me to bother to crunch their Pocket Empire stats to determine their available budget). Whatever is paid, whether in Credits, or with actual trade goods, may alleviate local shortages for that particular Aslan's family and home but unless we are talking gigacredits of pay, it's not going to make a difference at the Empire scale.
The greatest and quickest savings would be to scrap those non-Jump capable battleships and use that to fund the sped up tech uplift of Yero'ilra from TL 7 to TL 8 for 28 RU over 3.5 years and also the uplift of Eikhaaw over 3 years for 30 RU. Both can be done simultaneously. A slightly less unpalatable alternative for the military junta of the Glorious Empire might be to mothball those ships. This reduces the base cost from 3 RU/Size to 1 RU/Size (before modifiers for distance). That reduces the cost from 18 RU down to 14 RU and from 14 RU down to 10 RU, a savings of 8 RU for Htourlao. While that is still enough to do the sped up tech uplift for Yero'ilra (barely), there isn't much left afterwards for Eikhaaw unless then the Glorious Empire deficit spends. Of course even then, the net economic gains are still < 1 RU/year.
The economics say the Glorious Empire is doomed. Yet they are useful. For the Florians and Imperials they distract the Aslan and use up Ihatai who would otherwise cause problems, for some of the Aslan clans they serve the same purpose so who could help them.
The Aslan clans for whom they are convenient cannot without risking war with the other clans so I think they are out.
The Florians are best placed for it but providing subtle aid seems not to be their style.
That leaves the Imperium and the geography is terrible as is the blowback internally and with the Hierate if they are caught helping slave taking rogue Aslan. But I can see navel intelligence going for it. They would need a staging post and Tktk is well placed for Jump 4 fleet supply ships to move supplies to , if only the system could be kept secure and private perhaps by declaring a red zone and interdicting the system. So Tktk could be planned as a secret node on a supply chain to the Glorious Empire which I think could be an interesting opportunity for pirates, freedom fighters, journalists or honest scouts
The one action I can see that would pull the Glorious Empire out of its moribund death spiral in a quick enough timeframe is the retaking of Hliyh. A high population high tech world would provide enough RU to fund rebuilding the military (if it can be held). Given that the major capital ship assets of the Glorious Empire can barely move let alone conduct attacks, they would be hard pressed to actually win a war over Hliyh. They would also likely have to convince their opponents to go for Strictly Limited War as they don't want to damage the orbital habitat ring.
The Subversion Offensive option from Pocket Empires seems a better option than straight overt military attack. Subversion offensive in a best case scenario can lead to successful planetary revolt. In a more modest success, local Hierate military forces would take damage, as would Infrastructure (though the GE would not really want that). To fund the this subversion offensive though, those non-Jump capable battleships would have to be scrapped to free up RU budget.
A terror campaign of guerilla warfare and terrorist attacks by deep agents or left behind GE loyalists that were not important enough to be evacuated, but that still did not assimilate or switch loyalties. Even in a modest success, perhaps a weakened local Hierate garrison and fleet would be more agreeable to Strictly Limited War. Still slim odds...and of course the Hierate would likely grow suspicious if their military equipment and infrastructure starts blowing up, even if the culprits cannot be directly traced back to the GE.