I think the only good thing in this is that you are looking at a 16 month timescale for making a decision, until your fixed term deal runs out.
That gives you time to see whether he can save at the same rate (or whether his employment is more 'variable'). If he saved £10K in 2 months, at then end of the 16 months he might have another £80K, so circa £90K in total.
Your equity and his combined would be £440K. So based on % input, he might own 20% and you might own 80%. But then what? How much will you each pay towards the shared mortage - equal amounts? How much will you both have left to spend or save? How will you adjust the percentages over time if the value of the property changes, or if one of you adds savings to pay down the shared mortgage? If the roof blows off will you pay 20/80 towards the repair or equal amounts, or will he have more savings and pay a bigger % in return for a larger % share in the equity of your home? And so many other possible scenarios...
I think the worrying aspect is that your dp is either financially naive, or he is conning you.
Despite being a high earning contractor he comes to the relationship with no assets, no savings, and some debt. Of course there could be many understandable reasons for that. He made an extremely naive proposal that you would put in all the deposit (or 97%) of it, but in exchange for 50/50 ownership he would 'promise' to pay all the mortgage repayments.
Except he's a contractor, so may suddenly find himself not getting paid [that's what happened to me when COVID hit]. So what then?
Or after 2 years everything between you breaks down. He leaves with half of your £350K.
I know you're not going to do that @WhoevenamIinlife you're going to protect your deposit, but he is either very naive to make those suggestions, or very cunning.
It is also intersting that whatever you have suggested by way of alternative compromise, he has been instantly amenable to - whether that's TIC with different shares, or waiting it out for 16 months, or you both putting in the same amount of deposit and you doing something else with your remaining capital... All of these choices have different outcomes for you, and for him. They need really careful and well considered professional advice for each of you independently and together. So his quick agreement to each proposal again smacks of financial naivety, or possibly of him agreeing with whatever you say to gain your trust, stop you being concerned or make you feel you don't need proper external advice.
None of us know what the truth might be, but please be cautious.