That's one way to go. Another way, that doesn't require added weight, is to elevate the feet on a bench and do them very slowly, with a full range of motion, touching the upper chest lightly to the floor at the bottom of the movement and not resting for even a second with locked elbows at the top of the movement; fluid throughout. All the while observing the checklist I posted above. Depending on how slow I go, I can go to failure by about 20 reps, and I mean true failure. (Without a spotter!) Years ago, when I didn't have ready access to weights for a while, I used to do push-ups for reps. Many, many of them. But this is better.Push ups are a much better exercise then the bench press. You can use weights (put them in a backpack and wear the backpack) to increase the intensity. I personally do weighted press ups on gymnastic rings.
One idea is plyometric pushups.
The idea is that you not only need strength to bench press but power and plyometric push ups can work on your power to get the bar up with speed and can allow you to lift faster. I agree that doing 100 pushups with some ease will not translate into strength gains as your pecs are already conditioned. But people forget the power aspect of heavy lifts and plyo push ups really will help.
Do the down cycle of a push up and then explode up to a clapping hand or touch your shoulders. If you eventually can get 10-20 should touch push ups then try Superman push ups.
Instead of training your chest for pure strength, you can add the power element to get more press and lift more overall weight.
You don't want George on your team. He's a chucker.Plyometric huh?
"The muscle has to grow.... or die".

I had to youtube “Superman push ups”.Do the down cycle of a push up and then explode up to a clapping hand or touch your shoulders. If you eventually can get 10-20 should touch push ups then try Superman push ups.
I was in full beast mode today and even had to let out a manly groan as I benched. Not all that unusual at my gym,(World Gym), which doesn't have the Planet Fitness no groaning rules which seem idiotic to me, but whatever. Pull ups still suck. Can't do one good one, but I'm improving there too. Building more muscle and staying steady at the waistline. Almost look good naked, for an old guy, which ain't real easy.