That has cleared up one concern I had..
I would suggest replacing the ceramic block shown in your third image - You may need to partially dismantle the covers, but that would give you a chance to clean out dust.
The contacts inside the holder get burnt over time, and this could have been source of the smell - Look in the telephone directory and try to find an electrical wholesaler that stocks low voltage lights and fittings. You'll find them a lot cheaper than the likes of Clas Ohlson, and the staff will be better qualified & experienced in giving good advice.
If you can't find a suitable holder, I could source one in the UK and pop it in the post to (at cost).