dunno if your band will use a pa (a assume it will set mics up around to pick up the instruments) if so try playin your acoustic (im assumin its an electro acoustic) and try sendin it straight through the pa. iv known jazz guitarists do this and its sounds great, although he was usin an amazing jazz acoustic. oh an when you feed it through the pa roll back the treble and middle an try an get a very warm deep sound. if its not an electro acoustic, i always find a get a nice jazz tone if i again roll back the treble and middle on my amp an have the bass up high, i use an LP an it always does the job. it seems that you just need to thicken your tone, only play the solo on your LP using the rhythm selector an if it still sounds a bit thin roll back the tone pot a touch.

i dont think there's a chance that a distorted sound could ever sound good in that sitaution unless it was very subtle, ie only really distorting when you really attack the strings. couldn't comment on the use of your danelectro as i aint ever really played one and dont no what the sound is like.

but yeah all you need to do is go for the opposite of what you would do in a rock situation where you would increase the treble as you need to cut through a band. when your playin jazz it wont need to cut through in the same way, as long as you get good presence it will come through.