This might sound really dumb and backwards but have you tried tinned veg?
I found this works quite well with Flynn and he's happy to have his veg as fingerfood. Yes they are not as nutritious as fresh cooked and as adults we know that tinned veg are quite soft and bland but it's a start. It's kind of a step between mush and the good stuff and Flynn will eat them straight out of the tin not even heated up
not my ideal scenario but it gets veg in
If hubby and I are having carrots, Flynn gets tinned baby carrots as fingerfood (with some of our carrots hidden elsewhere
If Hubby and I are having corn, Flynn gets tinned corn kernels as fingerfood (with the good stuff hidden elsewhere)
If Hubby and i are having Mushrooms, Flynn gets tinned mushrooms as fingerfood (with the good stuff hidden elsewhere)
If Hubby and i are having peas, Flynn gets tinned peas as fingerfood (with the good stuff hidden elsewhere)
He's never had a problem with potato or pumpkin but if no veg are going in you can try this too.
Slowly we are mixing our own veg in so it's about half and half now and because he knows it's good he is starting to eat our fresh stuff first
It's taken about two weeks and I think I might be able to not buy any tin veg next pay... I think i'll have a tin of peas, carrots and corn in the cupboard just in case though
Could be worth a try...