Yeah furniture is often overlooked.
I remember chatting with someone who asked me what might be a reasonable upgrade for his set up. He looked at me weird when I said to try take away his super thick rug. A few days later, he told me that without the rug (hardwood) he did notice a significant difference where the sound almost echoed and was too airy. He agreed the sound was more muted with the almost half inch thick rug. He was buying a $1500(?) rug to replace his rug and somehow his wife signed off on the idea if she could select the rug. Weird, but he got the boss to sign off. So that's OK.
Oops, totally forgot to reply this post after first reading it. Did you end up buying the open back Sennheiser headphones? That one is a good neutral and great value headphone. Entry level you can get in for less than $200 CAD. I do find it surprisingly a little warmer than expected of a headphone of its design, but not bad. I have the HD565. I think there's newer models of it, but the overall experience is the same. The filtering of the outside noise wasn't great which kinda meant that since it was plastic, I'd occasionally hear sounds from the headphones from my movements.
The AKG K702 recommendation, I used to have the Q701 Quincy. Really comfortable, large and wide ear pads, but the headband IIRC was surprisingly heavy. Ears on average felt cooler than the others, unless the sessions got longer, then it'd feel warmer. I wonder if this is due to the fact they were 250 ohm headphones. Dissipating heat by removing these headphones was quite fast though. Clamping power wasn't as strong as many other headphones which is a pro vs a con for open back. Quite a bit more expensive, needs a bit more juice to power. I gave it to my bro for gaming/streaming/music and he really liked it. Less low tone outside sounds could be heard, but IIRC, the occasional tap from the wire tapping something on the headphone (easy mod if needed).
In the middle, I own and also currently use a Beyerdynamic DT990 PRO. Price point is in between the two other headphones. The ear pads are a bit unique in comparison to the others. It doesn't feel as much like foam. A neat suede type of ear pad material. Well build, slight edge to bass. I find the average temperatures on my ears for these are a little higher than the other two, but max temperature seems lower. I wonder if this is because this was the 80 ohm impedance version vs the AKG Q701 at 250. But I think the Sennheiser is lower? Not sure of the actual rating though I think I've read it's around 50? Very little stray outside low tone sounds and the design with padding, metal etc. means there's barely any audible noise from the headphone movements.
I mean, the point of open back headphones is not to isolate ambient noise by design. But this means less heat is trapped. However, I found that there's a basic level of ambient noise I'd like to isolate which are basic external buzzing of electronics and the sounds of the headphone materials moving I'd prefer not to hear. Beyerdynamic were a step up from the Sennheiser and IMO AKG K/Q are another step up, but all also have their own unique pros and cons. I used open back because I connect it to the TV for movies/gaming and I can still hear the kids if needed.