i think a percentage makes sense. get your house appraised, and then divide your equity by the appraisal

is the concern with your partner paying part of the mortgage pre or post marriage? pre-marriage, i would say look at comparable rentals and what they would have to pay towards that. post-marriage i would say draft a prenup where you get to keep the equity in your house and 401k as of the marriage date, and he gets to keep his 401k as of the marriage date. any growth/additional equity will be split 50/50

how much do you have saved up for a downpayment and furnishings? I think the reason behind waiting another year would be to shore up your savings. you're fairly new into this job (which was a significant pay increase) and looking at a house that is 50% of your net income. having additional savings would be a huge buffer and make this feasible