the 120V motors were made by merkle and multiproducts. The merkles were on the early games, and some had a smaller shaft diameter. I've seen people use collars to increase the shaft size so it's snug in the larger diameter cams.
the multiproducts motors came in a few styles, but were generally interchangeable albeit you may have to modify the motor mounting bracket to get the gearbox to fit or use grommets/washers to move the motor position so the roll pin hole lined up appropriately. There were also differences in torque and rpm between the motor model numbers/styles, so it's worth trying to get the right one if possible, but don't agonize over it.
the gearbox itself contained grease. Some people use very heavy weight oil in there to quiet the motor, but it will weep out. You'll see some machines with drip pans installed below the motors. Multiproducts recommended a synthetic grease called magnalube.
the blue 3-in-1 bpc recommends in the oil tubes is for the rotor bearings, not inside the gearbox...not that your gearboxes have a removable plug/screw to let you add lube - the merkles didn't and many multiproducts didn't either. The oil tubes just let felt pads inside the bearing carriers get wet. Imho, oiling is not a big deal on these. They are brass sleeve bearings and are self-aligning. If they are stuck in place, they are stuck aligned. The gear on the end of the rotor will wear out before the bearings do if you just hit it with oil every decade or so. Later model motors have no oil tubes for the bearings.
multiproducts has an agreement with pinball resource, so steve young can rebuild motors. Afaik, he isn't selling the parts you need to diy (mainly the rotor and the first reduction gear it mates to). If you wanted to buy enough motors, multiproducts probably still makes them. They used to sell small quantities, but it was too much hassle for them. Pricing for motors from pbr isn't ideal, so it's worth watching ebay for motors - they pop up occasionally...even NOS ones.
your mixer motor is a merkle. If it works (they collared it to upsize the shaft), don't worry about it. Your control unit motor is a multiproducts, not sure what your issue with it is, but it's the correct type of motor for bikini.
to be more confusing ... the motor output shaft fits snugly into the cam next to it and is pinned in place. The mixer/control unit shafts have a ball on the end which can handle small amounts of misalignment. The "non-motor" roll pin goes through the ball to allow some shaft wobble.