This is just my opinion. The aim is to get your money back asap without going to the tribunal because that takes ages and wastes time.
This is what I would do if I were in your shoes and can't afford a lawyer.
Print out 6-8 judgments so it is a thick bundle. Send it with your letter and in your letter add " As you can see from the case law judgements attached for your careful reading, you cannot withhold my deposit..." words to that effect.
I am telling you, when someone receives a stack of court judgments (even if it is not a solicitors letter) they will shit themselves literally , especially if English is not their first language. He can try to read it and be overwhelmed, or think do I need to see a lawyer, but that means paying money, but if I don't see a lawyer, crap, I might miss something.
Sending him 50 pages of judgements , will cost him a fortune to see a lawyer to seek legal advice. Does he want to pay to see a lawyer ? I wouldn't bother hlighting the important points for him because you don't want to paint yourself in a corner with the judge...just say here are some cases..(there are too many)
The aim is to overwhelm him and bury him in the paperwork. And so what if he sends a lawyer's letter in response to you ? so what ? you don't have to reply using a lawyer. Just reply yourself...but always be on the side of reasonable.
Also, send a copy by registered mail to the agent as well since the agent represented the landlord and accepted it, and ask him to pass it onto the landlord too.
Always be polite, be reasonable in your letter, because you are creating a paper trail for your own benefit.
Give a deadline to return the money and less reasonable costs for fixing. Say you are willing to discuss to solve the situation . Don't be rude.... I don't think you can force him to use your handman, but you can ask him to get quotes too...and then you guys can meet halfway.
Now, got to go feed the kids...good luck.
This is just my opinion (don't come after me if it doesn't work out)
Now back to the real world and got to feed my kids.