I'd recommend against the feet up benching. It is actually pretty complicated to explain because it's not a cut and dry situation (hardly anything ever is).
There are probably people who would be better off with their feet up due to lower back problems caused by etension/rotation problems. But those people may also be advised to limit flat bench pressing.
If you put up your feet it will limit your abilty to get in a proper position and provide a good stable "platform" with the upper back. It WILL limit the amount of weight you are able to push.
The problem is similar to the other side of the coin that you will see with powerlifters. They will really get their hips way up in the air and exaggerate their back arch a lot. Basically this makes it more like a decline bench and reduces stress on the shoulders and they can lift more. But as a general training technique this excessive arching should be avoided. What you want is feet firmly planted and a "neutral" lower back, which is one that is naturally slightly arched.
I noticed you said you don't want to arch your back. Can you explain what you mean by this and why?
When you put your feet up on the bench what you do is the opposite of the excessive arching thing. You flatten out your back. So it is no longer neutral. This impedes natural power transfer from the lower to upper body..a big part of benching. If you flatten out your lower back you also can't arch the upper back. Effective retraction of the scapula is impeded and this rouned back posture while lifting can cause the scapula to wing. Something you don't want.
So you want the knees bent, feet firmly planted, a good tight neutral arch of the lower back, shoulders down and back with scapula retracted (pinched) together...all this will lead to the best longer term "health". Especially at the shoulders. As well as the biggest numbers.
Maybe you can find something to place on the floor on both sides of the too high benches to place your feet on. Perhaps some extra plates or steppers. My bench is too high as well and I actually put my feet on gallon paint cans filled with sand
So whatever works.
BTW, I was posting at the same time as Ross and Pity so if any of this is a repeat of anything they said, my apologies.