I'm not the op, but being on friendly terms with people handling bids, doing small things even like helping them cross of simple policy things like "considering three options" can do wonders for your future bids.

Also constantly reminding them that you exist and are still in business...

I can't imagine you'd put in a bid if you're full up on projects, so you probably have some free time and putting together a proposal, even if it doesn't go anywhere (or perhaps especially if it doesn't) is you practicing your art.

You could use the proposal to show off new concepts you are trying to iron out, for instance.

Exactly. You want these people to feel a little warm glow when they think of you.

You don't do it as a specialized product company but do as a consultant of generic services where you compete by being friendly