Solo tuning is used to make the bass sound brighter so the sound carries better over the orchestra. If you can make yourself heard and can find parts in the right key, there's no reason not to play a concerto in the lower tuning. If you're just using piano accompaniment your options are much greater. There are orchestra tuning piano parts for most of the best known concertos.
Here are just a few readily availble concertos originally written in orchestra tuning. If I can think of some more I'll post them.
Robin Holloway -Boosey and Hawkes
Serge Lancen - Billaudot
Gordon Jacob - Yorke Edition
Alan Ridout - Yorke Edition
Andrei Eshpai - I have a scan of the piano version. Haven't found a copy for sale anywhere.
Armand Russell's "Harlequin Concerto" is a good piece, but no copies to buy that I know of. He's still alive and kicking, so you could contact him.
I don't have the music in front of me, but I think the Rota "Divertimento Concertante" is in orchestra tuning. Carisch Verlag (find it on sheetmusicplus)
More if I think of any.