I'm finding it hard to fully understand your post, so bear with me, and apologies if I'm getting the wrong end of the stick.
First lender said the house wasn't worth what you had offered on it. ?
Second lender also said they'd give you less money than you had hoped and stretch the term but they'd lend you more, but not the full amount. ?
Is this all on the same house?
One of two things seems to be happening:
One. The Estate Agent is vastly over-valuing the house to get people to sign up with their business. This happens all the time.
Two. You are pushing your finances to the limit and it's on a knife edge whether bank two will lend to you.
The other possibility is:
Three. A combination of both of those things.
Now, I have Property Log so I can see which agents are vastly over-valuing properties by the amount they're forced to reduce them by; how have you priced up the value of this house, and do you think it's worth what the sellers have accepted from you? I did a little pricing exercise this morning via an agent I already knew to be overrpricing in an area I'm looking in. Original asking price of a house I'm interested in started off at 36% more than the asking price per sq ft of other locally advertised properties in January.
In fairness to the agent, it's because the owner bought at the top of the market and everyone else selling their houses did not (properties last bought in 21/22 are particularly problematic in this respect).
Banks hate overpricing, but if you're on a knife-edge with your affordability, they will take it even more seriously. Is that maybe the case?
As to your current versus future housing situation, it's a far from desirable thing that I'm about to suggest, but a lot of people do it: you tell your landlord far closer to the time that you can't move out from your rental and he has to tell his buyer that they're going to have to wait. There's virtually nothing he can do to get you legally removed from the premises within a timescale of about 6-9 months anyway, because the courts are so backlogged.
Like I said. It's not desirable, but home buyers do it, because our house buying process is so utterly messed up in the UK.