I'm not clear why those on the front should be a problem but yes, the one at the back is not very accessible.
I agree with not wanting to risk swarf in the oil ways.
My Myford lathe and mill have those ridiculously tiny sunken buttons things as oilers, and I've not found any sensible way to use those. They seem to need a special oil-gun with a very fine nozzle, and I don't have such a thing. I've not found any problems just winding the saddle or table to the ends of its travel, putting a small pool of oil on the ways in front of its return travel; moving the unit to its other extremity and repeating for the opposite side and direction. Inspection afterwards shows a practically uniform oil film over the entire surface.
(It is important to wipe the surfaces clean first.)
The Harrison L5 lathe uses mainly oil-cups with hinged lids. Might it possible to fit similar on your lathe? These might be available from cycle dealers.
Some oiling-points on the L5 are simple holes with countersunk entrances, but they are not ideal.