Honestly, I think you are neglecting your pull chain by not doing some sort of pulling movement. The pull chain could broadly be thought of part of the forearm, biceps, rear deltoids, lats, traps, rhomboids, and some smaller muscles. This represents a big part of your upper body musculature, and could be thought of as the other half of what the press-ups hit.
A lot of people argue that we need to do at least as much pulling as pushing, maybe more, because of our habits of sitting and the resulting kyphotic posture. I haven't dug into the science there, but to me it makes sense that a balanced program should at a minimum have a squat, an upper body push, and an upper body pull.
There are a few ways to get around the limitation. One would be laying underneath a table (if you have one at an appropriate height) and doing rows. Another is to get some sort of setup with a band that you can anchor to a high-ish anchor point and then do rows. If you google "DIY rows" or "no equipment rows", some stuff should come up.
Another solid option would be to use a suspension system. I like NOSSK's Twin Trainer Pro. For $50 (or less if you want to DIY!), you could have the NOSSK system and hang it on the other side of a closed door, and then use the handles to row. See this video to visualize what I'm talking about, at around 3:30 you get a sense of how it anchors:
https://www.youtube.com/watch?v=b413J7bWyuc
The product link is here. The various images they have show how the device can be used, 5th image shows somewhere rowing (but with a different anchor use):
https://nossk.com/nossk-twin-pro-suspen ... p-trainer/
I won't go too much into it in this post, but these sorts of suspension systems (NOSSK is just one, TRX is the expensive brand-name one) are like gymnastics rings and open up a world of bodyweight+ options that allow you to hit your whole body. For a fairly small amount of money, you have a portable gym. Something to consider if the other options don't work out.