Putting a generous settlement offer in a letter before action

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I have an ongoing dispute with a trade, where they did an unsatisfactory job, promise to come back to resolve it but simply never turn up (five times). I paid when they did the unsatisfactory job, without living for the work for any amount of time to realise how completely inadequate it is. 

After today's fifth no-show I'll send them a letter before action tomorrow.

Can I put a settlement offer in the LBA to encourage a swift settlement, but then go to court for more than that if they decline the offer? Could this potentially bite me later?

At this stage, I would take a refund, and appoint someone else. I think I would be entitled to claim for the cost of someone to finish the job and fix the associated damage, even though this exceeds what I've paid. Really I don't actually want them to give them further opportunity to fix it, but recognise that I need to. Here is an excerpt from my drafted LBA:

"The key issues with the job carried out are:

1. [redacted]

2. [redacted]

3. [redacted]

Without prejudice to future court action, and in the spirit of resolving this swiftly, I am prepared to settle this claim, at this time, for a refund of the [amount] paid. If you do not accept this offer and/or court action is required, such court action may be for the full value of my losses which may include:

-The full cost of another trader to remediate the work, for which I have been quoted [1.5 times amount above]

-Damage to my property including... [redacted]

-Legal or professional fees in relation to a court claim"

At the end of the letter I tell them their options are to accept the settlement, fix those numbered issues or ignore the letter and get slapped with a court claim. 

Does this letter look OK? Would it potentially corner me into accepting (just) a refund if we ended up in court? 

Doozergirl

Sound alright to me.  I think 'without prejudice' is the key phrase.