Hi lefthander - an obvious bias here, but I do believe the K75 to be more than capable of towing an appropriately sized trailer - it has adequate power, great fuel economy and an available hitch that was designed for the bike (namely the Reynolds) which is single-sided ie rear wheel can still be removed if required and has 5-pin wiring (allows for aux 12v power). Here are some other thoughts on trailers based on earlier research (I had planned to do some long-distance touring this year but plans got thwarted, on many fronts ... alas) :
1. Size? A smaller/lighter trailer will tow better. Figure out what would likely be your minimum requirements - for my purposes this was to be a solo trip with ~ 12 to 15 cubic Ft of gear.
2. Weight? I

something up to 150 lbs un-laden (~300 lbs loaded max). There are some open designs (eg Bushtec Spartan) which are light but obviously less secure
3. Hitch-height? The Reynolds (for example) has an installed height of ~ 13" so I upgraded the 8" trailer wheels (approx 10" hitch-height) to better 12" wheels (approx 13" height) to match the hitch
4. Suspension? I came across a lot of (usually older) trailers that did not have any (ie just a solid axle) ... opinions may vary on this but in mine, should have some kind of suspension
5. Make sure the trailer has a swivel-hitch (as all m/c trailers should have) - alternate "utility" trailers (for atv /small cars etc) are usually standard (ie non-swivel) type.
6. I had also planned to upgrade standard brake-lines to braided ... something that is probably a good idea (if not done already) given the additional trailer weight and age of our bricks now.
Just like any oil or tire thread - there are a range of opinions / experience out there - so do your research and make a list of what's important to you.
Hope this helps - and happy to answer any other questions you may have regarding the Reynolds. Due to circumstances, I also have the trailer I purchased to use with it listed locally (it is a registered m/c trailer but could also be used for other purposes) and will share that link with you (via PM) so you can visualise the above considerations, for my own plans at least.
Keep us posted on your project!
Gio