@Thomas Wright I have found that performing push ups has helped my overhead pressing tremendously.
There are a lot of ways to structure this. You could add push ups to your warm up (you could also emphasize the floor press before each TGU on S&S days,1-3 reps before each get up will add some horizontal press volume without taking away from your get up). You could also perform them GTG style throughout the day or perform them in a different session.
What I've done for about the last two years is use pushups as part of a morning recharge. I'll set a timer for 5:00 so that I don't get too carried away, when that timer beeps I'm done. If I'm performing a structured workout I'll do that later in the day too.
Since I'm not a manual laborer and most of my programs have a limited number of movements in them I like to use a large variety of push ups to provide me with a little movement variety. Instead of chasing numbers I'll just perform whatever variations in whatever quantities feel good that day. Some days I'll feel like working on strength and I'll add weight or perform 1 handed push ups, other days I'll chase a pump. Sometimes I'll work on developing mobility. I have yet to get bored this way.
I rarely press overhead any more (it's just not as fun as it used to be for me) but I've been able to maintain my strength to the point that when I have to press 1/2 BW for my L2 recertifications I just need a few weeks practice to hone the movement.
If you're interested here is a little article that I wrote about push ups a few years back. I hope that you enjoy it.
Why The All-Time Greats Love Push-Ups, And You Should, Too
Cheers! Let us know how it goes.