Hi Mike.
Welcome to the forum.
I've a Hobbymat BFE65 of late-80s vintage bought new. It's the Mark 1 version with a 4-speed lever gearbox. As you say, the manual is pretty non-specific as to the type of oil/grease to use. For the record all it says is:

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and

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I must confess all I've ever used for rust prevention/oiling the slideways is a general purpose oil acquired long ago. For these purposes, a recommendation I often hear nowadays is to use SAE30 lawnmower machine oil.
As regards the milling head internals, in some ways the BFE65 resembles a poor man's EMCO F1/FB2 but the lubrication regime is different. The EMCO machine gearing runs, I believe, in an oil bath that has to be replenished/refreshed. I had occasion to open up the Hobbymat head 20 years ago when I had a problem and found that the gears (phenolic composition) were simply smeared with what appeared to be conventional bearing grease. I used this when completing the repair. Incidentally, I'm assuming you likewise have the geared head — the later Mark2 Hobbymat had a belt-driven arrangement for which the lubrication regime may be different.
Your CNC conversion sounds very interesting — I'd love to see a description (with photos, please).
Joe