The trekking bars you linked you *should* be able to use your MTB brakes, shifters, and grips so you shouldn't need to replace anything just to make it work.. unless as you said your cables won't reach.
If you wear gloves (I recommend it), you can probably get away without any tape on the rest of the bars for now.. and add it later if you know you want it. You can do the tape yourself.. it's not actually that difficult (I'd recommend non-adhesive tape.. that way you can wrap and unwrap as many times as you need to get it right).
I just replaced the flat bars on my hybrid with some soma sparrow bars which put my hands/wrists at a much more natural angle when riding... and I taped up the whole bar, which was kind of tricky since I had to go over my shifter/brake mount, which isn't really designed to be taped over. I installed mine as drops, but they can be set up as risers too.. if you search google images or flickr you can probably find a lot of examples. I'm really happy with it so far, even though I've only ridden about 20 miles with it set up like it is.
I considered trekking bars, but I wasn't sure that they would really fix the specific problem I was having, which was numbness in my hands. The sparrows fixed that, they also shortened my reach and dropped me into a more aerodynamic position (I can really feel the difference in headwinds).
It may also be possible to just swap out your current stem with the bars you already have to something shorter or with more rise.. you may find yourself wanting to change the stem even with new bars.
Oh, and to answer the road bike question.. you can use shims with MTB bars and use road components, it's really the other way around that becomes problematic.. since you can't fit MTB components on road bars. I think odds are really good though, that if you buy a new bike at some point, you'll be able to work out the fit so that you aren't having to immediately swap out parts. Or at least, that seems to be how it is for most people.. not for me, but I didn't start to have issues until about 45 minutes into rides, so it's not something I realized would be a problem at first (and I think really, it just comes down to my stock flat bars just being too wide for me - if they were 5cm narrower perhaps, I probably wouldn't have had any trouble).