I'm going to start by saying this is said with a friendly tone and is for food for thought and not intended to be accusatory.
You have done an amazing job of getting £200k of equity in your house and be in a position to be mortgage free as young as you are, however, is it possible that the situation you have found yourself in as come at the cost of this?
Sinking all of your cash into the house has left you as you said in your opening post as being asset rich, cash poor and then when work was needed on the house you were then having to take out loans and credit cards to cover the costs. This has given you less security not more. It's also put you in a position where you haven't felt able to start paying into your pension and as a result having been missing out on spectacular employer contributions jeopardising security in your retirement.
I don't know, nor need to know, the circumstances of how you got into the debts but from your opening post you said yourself they were needs not wants. It sounds a bit like you have been living a bit of a save-use-credit cycle and this has given you less financial resilience to those emergencies.
Don't overpay your mortgage at the cost of not being able to weather the storms. Minimising the cost of the additional mortgage by overpaying that somewhat make sense but maybe let the primary mortgage run it's course?
We are in the fortunate position of having quite a bit in savings and we have contemplated overpaying our mortgage more but for now we haven't. Last year my car looked to be terminally broken although the problem ended up being quite an easy fix (aside from it being off the road for over 6 weeks, purchasing and returning 3 different parts that didn't happen to be the right part and the end wait for the correct parts to be posted from somewhere in Europe). It was reassuring that should have needed to replace it, I could have done so without taking on more debt. The year before that our garage roof needed replacing and we were able to pay for that without using credit.
Having savings gives you options, as you've found it can be a bit trickier when a your cash is in your home