Good idea to sort it out face to face, your approach sounds very reasonable, hopefully you can work this out.
She may or may not have thought of, or, as you say had it pointed out to her by others, about the inheritance tax situation (among other things) and that you may end up better off from a tax point of view, if - and there's a lot of ifs here - the house is left or half left to you, it's over three years since you moved in, and that the exemption still exists.
You could of course split the tax bill between you but I'd be very careful about committing to that now - in case any confusion that should the tax bill not arise and she may think you still owe her X amount, also you don't know your situation at that point in the future, and (probably unlikely but) the rule could change and therefore the scenario could change. Not to complicate things further but if her half of the tax bill was more than 30k that would be above the limit for her to receive a gift from you (which it effectively would be a gift) then she'd owe CGT tax on the portion above that.
Don't be too casual about offering to pay / split tax bills - it could be a very large amount depending on the value of the property at the time and the thresholds at the time, and whether it's left to one of you of both of you. (As you each have an exempt threshold amount)
Oh dear, have I given you more questions than answers, sorry, hope some of it helps!