Mainly from Armitai-Preiss and the articles he references in "Mongols and Mamluks: The Mamluk-Ilkhanid War, 1260 1281".
Sultanate of Rum allies
The army that Hulegu led into Syria in 1259/60 CE included Armenian, Georgian and Seljuq allied contingents, the Seljuqs were led by their joint sultans. Would suggest that at this time all of these should be allowed to be used together, at present only Georgian and Armenians can be.
Seljuqs again appear in the army that fought at 2nd Hims (aka Homs) in 1281CE - again with Armenian and Georgian contingents both of which were led by their kings. However, by this stage the Seljuq sultanate had collapsed and I would suggest that the Early Turcoman Beyliks list would be more suitable for this ally as Seljuq remnants. Suggest this is used from 1277 Ce to 1281CE as an allied contingent - I've not seen anything that would suggest an allied contingent after 2nd Hims in 1281 CE.
Armenians
Armenian allied contingents were common in Ilkhanid armies, usually led by their king. However, at Ayn Jalut only 500 Armenians were present which IMO does not justify a contingent, just a TUG. Presumably the larger contingent that Hulegu had before heading back east either mainly stayed with him or went home and Kitbuqa was left with only a small number in his army of 10-12k.
Suggest that a single unit of Armenian cavalry be allowed in the list but that it cannot be used with an Armenian allied contingent.
Crusaders
IMO this is problematic as numbers of Franks in Ilkhanid armies are hard to pin down - they may well have been quite low and what we have in the list (like other rule sets Ilkhanid lists) is a rather optimistic over-representation especially for knights. Armitai-Preiss suggests that any knights present may well have been small numbers in the troops supplied by the Armenians coming from Frankish held castles in Armenia.
Given list policy it is probably not a realistic option to remove them currently. However, I would suggest that they should have an end date as I don't think any material number of knights would be available for the whole length of the Ilkhanid list. The fall of Acre in 1291 CE may be a suitable date. Crossbowmen on the other hand are attested to 1307 CE at least.
Bit more on Sultanate of Rum allies for Ilkhanid.
In 1277 CE both Georgian and Rum allies were with the Mongols. In the Battle of Abulustayn that took place during the campaign the Rum troops stood apart and did not fight - a hesitant ally ;D
BTW the Sultanate of Rum list itself should run to 1277 CE not 1276 CE as it was after this battle that it finally ceased to be an effective state able to function independently (well, independently-ish as they had been Mongol clients since 1243 CE). This would mean that Early Turcoman Beyliks should be used for allied contingent after 1277 CE and not from 1277CE as suggested above.