Sounds like your Meochrom is indeed much older than the ones I have used. Sorry for the unfounded optimism!

The usual thing with any low-voltage, high-current halogen socket is due to the temperature - there can more easily be a little bit of corrosion on the socket or bulb-contact. That puts the resistance up a fair bit so you get a much hotter socket and probably a lower current through the bulb. The halogen bulbs I have used in enlargers are different sizes, but have all had the standard two pin connector on the back. It looks like two little rods and these slide into a ceramic socket with springy contacts inside. The socket itself usually has heavy multi-core cable which is connected to the rest of the device with screw connectors, or some proprietary equivalent.

Over here we have the second-hand boards with plenty of meopta parts and enlargers. They were very popular in amateur use as they are well made and lined up accurately (in my experience, ymmv as they say). Maybe you can replace the whole enlarger for thirty euros or so? That would make much time or money expenditure, on repairs of the current one, less practical perhaps but it is an option.

If I see an older pattern of head for sale here I will let you know. They don't weigh much after all, so long as I didn't need to send the transformer!