Here’s a what I do in my industry: Architecture. I refuse invitation to tender for services where there are more than 3 bidders. I phone the person managing the tender and ask if they have a preferred Architect already and I say that I don’t mind if they do and I’m happy to provide a tender so they can show they’ve tried to get 3 bids but I would rather not waste a week putting together a proposal and a concept design etc. This works well for me.
Open tenders are typically won by firms that specialise in scatter gun bidding and the results will usually be poor quality. A firm with a good design track record doesn’t need to win work this way so they won’t waste time on them.
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.
Open tenders are typically won by firms that specialise in scatter gun bidding and the results will usually be poor quality. A firm with a good design track record doesn’t need to win work this way so they won’t waste time on them.