You might think of this from a different perspective- NOT from TVs to speakers but from sources (of video you want to show) to TV and speakers
separately. For example, what feeds both TVs video? An AppleTV that you are switching back and forth? If so, let it be the link to the HP audio (connect the HPs to it). Then it can move back and forth between the 2 TVs and the HPs will be the speakers with whichever TV you are watching because they connect to that AppleTV.
I'm guessing each TV receives its own source (of video) and thus, the origination of sound you want in the HPs starts there (maybe TV apps?). If so, HPs don't seem to be a great fit for your situation. Instead, get yourself a receiver and a few good speakers for Home Theater purposes. Receiver can then be the "central hub" through which ALL video and audio can enter and then be split out to wherever you want it to go. For you, the audio would be routed to dedicated speakers, shared with all sources (2 TVs, 3 TVs, 4 TVs, Blu Ray, Game Box, Cable/Satt, AppleTV, etc.- a good receiver could easily have 4-8 HDMI inputs). All sources route INTO the receiver and then the audio gets split away go to the dedicated speakers. If you want HP stereo speaker sound, get yourself only 2 good speakers for that receiver. If you want better than stereo, just about all receivers will likely support at least 5.1 surround sound, so perhaps start with 2 speakers (stereo) and then add on over time (center, sub, left surround, right surround).
HPs are NOT made for these purposes. They are only intended (by Apple) to be stereo speakers for use with Apple hardware (and mostly Apple services). If they had ANY normal input (the much wanted AUX input to bypass the "smarts"), they could sub in for the speakers attached to a receiver in the above scenario. But Apple likes its tightly walled garden and that lockdown works against this kind of use. Put in an AUX and long after the speaker is made obsolete by lack of software updates if not outright abandonment/vintaging by Apple, the speaker probably gets continued use for upwards of a few decades. No AUX jack means the push to replace them more frequently can be triggered by lack of software updates/vintaging/etc (like phones and Macs).
The most compatible option if you want to force HP use is to:
- Think of the TVs as the end point for the video.
- Think of the HPs as the end point for the audio to either TV.
- If the source for what you want to show on those 2 TVs can be an Apple iDevice or two AppleTVs, you can take UI steps to switch them for each TV... basically (you) standing in for eARC automatic setup with some manual clicks to make the source Apple device use the HPs in a "take turns" approach.
If you want eARC simplicity (automatic switching), the receiver and dedicated home theater speakers will do that trick. A possible cheaper option would be a home theater soundbar with at least 2 HDMI inputs for each source (for each of the 2 TVs).
- Video source for TV #1 connects via HDMI to the soundbar (or receiver).
- Video source for TV #2 connects via HDMI #2 to soundbar (or receiver).
- Audio from whichever video you want to watch on either TV right now is played on the soundbar (or receiver speakers).
The downside to this is that placement of the soundbar becomes an issue, else sound may not seem to be coming from the screen but to the left or right of the screen because you are trying to share one soundbar. Maybe TV hanging over this multi-input soundbar hanging over TV #2 (a soundbar sandwich if you will)?
This all presumes you are wanting to watch and listen to
ONE thing at a time. If you are actually wanting to have TWO things on TWO TVs with audio at the same time, think 2 soundbars (or 1 receiver with 2 "zones" and at least 2 more speakers hooked to zone 2 terminals, and then both zones turned on at the same time). Each soundbar (or receiver zone) would play the respective audio at the same time.
OR, if you have a favored TV and a less important one, maybe link AppleTV to HPs to the favored one and just use the less important one's TV speakers for its audio. Favored will sound great because its got the good speakers for audio. Less important one will sound relatively terrible but you'll be able to hear its audio even on crappy TV speakers.
Lastly, if the goal is both TVs simultaneously and you have a "use HPs or bust" mentality, think 2 AppleTVs and 4 HPs (a stereo pair linked to each AppleTV, for basically two fully separate setups).
Personally, I think of HPs primarily as (Apple) music players, which is the intended function and there are not even any rumors saying anything different. "We" have tried to force them into being Home Theater speakers but they are not really intended for that, nor are there any rumors implying Apple is working toward that goal too. Yes, they (as would anything else) be a big audio improvement vs. leaning on the stock speakers within a TV but there are PLENTY of fish in this sea.
Other options offer real/pure focus on home theater audio. And when I read setups beyond very simple (like one screen), I immediately start thinking "central hub" (receiver) for managing the switching and efficiently using one great set of speakers for a variety of AV sources. Your post reads like you need to go this way unless you are mentally locked on using HPs. If so, you need to embrace manually switching what (Apple) source is using the speakers instead of the eARC automatic switching you may be seeking.
I hope this helps.