Richard, it's the mis-match between the pickup and pre-amp impedances that causes problems. A UST usually has a 10 Megohm load which matches the input impedance of most pre-amps. The K&K is 1 Megohm - a mis-match by a factor of 10. If you solder a 1 Megohm resistor across the terminals in one of the jacks on your guitar lead, that will correct the mis-match and improve the performance.

Or, alternatively (the best alternative, IMHO), you can use a dedicated pre-amp with a 1 Megohm input impedance, such as K&K's own product or, as I do, use an active DI box (which, after all, is just a pre-amp without any knobs) with a 1 Megohm input impedance such as the Orchid (which ties in with your second point!).