1982 XJ750 I'm trying to install the carb to cylinder transition piece Xj750

NA 1982 Xj750 Seca

I'll call it the manifold boot, seeing as it is both a boot and a manifold! Huzzah! I'm trying to install the manifold boots (x4) with everything spacially inhibiting already installed on the bike and as you may imagine, it's difficult. I have the airbox to carb boots fully in place and attached to the carb, so I'm trying to link that last gap with these manifold boots and it is really hard with everything else in the way. What is a more possible solution to re-installing the carb? Also any advice on how to seal the manifold boot to the engine? It looks like it would leak terribly if just simply put back together as is

 

You should fit new gaskets to the inlets. You would be better removing the carbs to give you working space, fitting the inlets and then replace the carbs and fit the air filter side to them. That is the way I would do it. You could try slackening the bolts off on top of the airbox and push it back a little to see how much space you have but removing the carbs is best.