I know, and I do understand how very difficult that makes things. Not least because if it wasn't your DS, and he is currently making an effort (working etc.), then accusing/suspecting him seems especially unfair.
I think these kinds of uncertainties cause a huge amount of difficulty and upset... The death of trust in your own DC is very painful.
That is one of the main reasons I fitted locks, and continue to lock my money away: I don't want to give my DS any opportunity to steal from me again, because the suspicion of theft is actually worse than the loss of money. I suggest you do the same, whether or not you can 'prove' anything...
FWIW, I didn't notice a difference in behaviour when my DS was stealing from me, except that (with hindsight) he was getting wrecked more often... But he wasn't more guilty, or defensive, or anything like that... And he still went to college, and sat down with us for meals occasionally, and celebrated Christmas, and... and... :(
Some other snippets of info that might be relevant...
My DS stole over a grand in 6 weeks. He was putting about £90 of M-CAT up his nose per night during the Christmas hols... And he had 'debts' and 'favours' to repay, and was inclined to be 'generous' to others who had been generous to him in the past...
He was already in the habit of selling his stuff to buy drugs, and I naively assumed at the time that he was simply selling to other young people. But in fact, he had connections with a 'fence' - i.e. someone who was buying and selling anything/everything, no questions asked, including stolen goods. I found this very shocking, when I discovered it. The chances are your son knows someone like that too... The 'exchange rate' from such people is (naturally) very low indeed, so having a ready source of money and being able to avoid him was definitely attractive to my DS...
Though of course, if your DS has stolen the money, and hasn't spent it all already, it would be easy enough for him just to have set up a bank account...
I don't know about involving the police. It feels like it ought to regain you some control, but it probably won't: if DS didn't take the money, and you've just lost it, you are going to look ridiculous; and if he did, unless you have proof and want to press charges, there is nothing the police can do.
There are considerable disadvantages (I have discovered) to putting your DS 'on the police radar'... We still get fairly regular visits because he is on their 'list of suspects', although it is 5 months since he was in any kind of trouble.
Sorry. I'm probably not now helping, am I? I'll shut up. 
Thinking of you.