Investment & Investing

Looking to move in a couple of years so would also increase our LTV for that.

Doesn't matter too much there - if you've saved elsewhere you can always just pull the money out and use that for the deposit and you've got your better LTV that way instead.

It's the usual tradeoff.
Paying off a 3% mortgage is a very safe way of investing at 3%
Putting money into a tracker/stocks/shares is a less safe way of probably making more than 3% but maybe not if the markets go weird.

Right now obviously the markets are very volatile. So you've got a good chance of making quite a bit if they recover and a good chance of losing quite a bit if they tank again at the wrong time.

So it's entirely down to risk appetite.

I overpaid as much of my mortgage as I could when I had it and I don't regret paying it off.
If I'd tried to get clever and put that money into shares or something, Covid would've tanked them and I'd still have a mortgage.

It doesn't, but then it is a simplistic model that can't take into account all permutations of people's circumstances.

It seems that you're already thinking along the lines of reducing total interest paid, and the way to do that is to overpay.

The reasons for not doing so would be 1) utility of liquid assets (you need cash now for some reason) or 2) you can earn better rates of interest elsewhere, that can offset the interest paid (including transfer costs), without any appreciable increase in risk.

2) is hens teeth.

[Edit] The alternative would be chucking it into your pension. The best comparison would be to a spreadsheet showing you the net present value of both.