If you want to increase your bench, why toy with the idea of dumping the bench at all and replacing it with dips?
How much do you weigh now?
3x3 at 225 is obviously not ideal if you're only going to bench once a week. You need more volume, as you noted. If you're only going to bench once a week, I'd switch to doing 5x5 on bench and doing your dips 2-3 days later. So, bench 5x5 on Saturday and do your dips on Wednesday, for example. I think you can slowly make some bench gains that way, or at the very least maintain. It's not like that strength is gonna go away so fast. I took two weeks off of benching and lost maybe only 20 pounds on my bench for sets of 5, and it came right back even though I'm taking it slower.