Linux can be run on an Nintendo 64. Mainline Kernel support has been added in v5.12
At least with Firefox Quantum (v57) they have tried to continuously bring in optimizations to bump the performance. In the meantime there has been lots of work with WebRender, a newer and more robust Javascript Engine and better CSS engine which made it get faster every update. Being quite fast and snappy isn't just a placebo since Firefox has lately started to get better Speedometer scores than Chrome
What you could do is have one of the HAs install the custom integration remote-homeassistant. However, even then it would mean that you have to somehow make your instance available outside e.g. VPN, port forwarding, cloud service, ...
This one connects with the instance directly via a long-lived token and allows you to control and read date from the other instance. The good thing though: The configuration.yaml way allows you to specificially include or exclude entities. So with that you could technically only send the entities from slimmelezer+ without having to pass the other info.
I would say the only caveat would be that because the long-lived token is somewhere on the other house's instance, they could technically take it and send commands randomly to your instance :P Maybe with an extra user you could maybe limit the permissions or something similar and create the long-lived token there - haven't tried it though, just a thought.
Since the Hue bulbs are using the Zigbee standard, you can still safely buy them in the foreseeable future and just connect it with something like SkyConnect, zzh!, Conbee, etc. and use it with Home Assistant