Oh dear ocelot, I do feel for you!
You can express your wish to exchange by end of May which does let them know that you're anxious to proceed, so no you are not being unreasonable. However, the solicitor acting for the ftbs will not be pressured into exchanging before they are ready (they have to act in the best interests of their client), so your wishes although noted, will be ignored if it is unrealistic to exchange then.
The survey has a section (I) which lists points to raise with their solicitor.
The searches also may reveal planning permissions, building regulations, any environmental issues etc.
Both of these can mean further additional enquiries and evidence might be necessary.
Sorry, not much help but it's difficult to know how much legal work is still to be done, as the survey and mortgage don't really give an indication.
I think you are too far down the process to walk away and it sounds as though the ftbs are committed, albeit slowly!