First off, I don’t have your lathe nor have I worked on that particular model. However, I have worked on quite a few lathes and gearboxes through the years, so I’ll give it a shot.
First regarding your current problem of reassembling the feedbox cover – Make sure that each feed gear is engaged in a particular position and that the corresponding knob agrees with that position. It is possible that you’re just out a gear tooth or two on the shifting rack. You may have to try a few different combinations to get the correct timing. You might also consider doing a dry run with no gasket or sealant.
I also noticed that the shafts for the shifting blocks are secured in the feedbox at the castings with what looks to be a set screw. It is possible that the position of these shafts has been rotated or shifted during a reassembly attempt?
Also, I wasn’t sure whether the gearbox cover was pinned or dowelled. If not, you may need to try shifting the cover around to get the position right.
As far as the leaks go, this is what I would do. Pull the feedbox off the bed and set it on a bench. Then clean the headstock and everywhere you can reach and make sure oil isn’t running down from the headstock.
I would probably completely disassemble this feedbox, but you may not be comfortable with that. Just remember that fixing leaks is all about cleanliness. At the very least, wash out the bottom of the gearbox with some brake fluid and dry it, and clean off all the paint on the mating surfaces. I make my own gaskets either with paper gasket material for precision surfaces or rubberized cork for covers and non-precision surfaces. Also ditch silicone sealants and consider using Hylomar sealant. It is much easier to work with on machine tools and less likely to contaminate oiling systems – especially in headstocks.
I would get rid of all the Chinese-made seals and replace them with good quality seals. You may be able to reuse bearings if they are smooth, but a better choice would be Koyo or SKF, but of course that’s your decision.
Pull any endcap bearing cover and reinstall with new gaskets and Hylomar. Also check that any through bolt holes are either sealed with Hylomar when they are cleaned or use copper compression washers. (I make mine.) And don’t forget to flush the blind holes with brake fluid and you might run a tap through them.
If all your mounting bolts are external, you can put the cover back on while the feedbox is setting on the workbench. It would be much easier to get everything aligned and shifting correctly this way.
Also regarding headstock covers – if this is just a gasketed cover, I usually make a rubberized cork gasket, clean the headstock cover mounting surface with lacquer thinner to get off any oil. Then use contact sealant on the headstock cover sealing surface and install the cover gasket on this surface, remount the headstock cover and let it set overnight. Next day pull the cover off and smear a little anti-seize on the face of the gasket (not too much). This will make the headstock cover gasket where it won’t stick to the headstock thereby making it reusable without any additional prep.
Venting shouldn’t be necessary on an oil lubricated headstock in a lathe. All that I’ve ever seen use a labyrinth seal front and back on the spindle. This is a wet side/dry side seal. It by nature has a gap. Excess pressure in the headstock vents out of these seals. It is a non-contact seal.
I know this is kind of long, but leaks can be complicated. Never let anyone tell you it is just a leak.
After I’ve written all this, I had one more thought. Since this is a brand-new machine and I assume still under warrantee, is it possible you could send the feedbox back to Precision Matthews as a unit to be either repaired or replaced?