Hoi Henno!

You could look for an signal matching adaptor; I found one that is suitable for FM, which is just a small coil transformer that allows you to adjust the amount of signal going through it. This is an off the shelf module from my local electronics shop, but it was big-time expensive. When I opened it, it was just a miniature FM tuner transformer and a couple of connectors, which could have been bought seperately for about a quarter of the price as loose components. If you're not scared of soldering, then all you need is a miniature FM tuner core, a bit of shielded 75 ohm coax and two connectors. If you are interested, I could try and sketch this and post it here.

It was an Altai brand; I didn't use it after I found I could just collapse the aerial to half it's length and get excellent results.

Are you sure that the built in antenna is not adjustable for RF gain? My friend across the back here had a Volvo amplified antenna built in to his car that we discovered could be adjusted with a little twiddle pot on the case.