do you suggest I take them both completely apart, or take off the float bowls and clean the jets while still on the bike itself?
I think I'll do the float bowls first, see if that solves it - if not, take them apart.
Being a total mechanical novice, the prospect of dismantling things is a little daunting - but I'm also pretty eager to get my hands dirty
Avoid using carb cleaner on anything rubber or plastic.
Remove the diaphragm covers and inspect the diaphragms for cracks or holes. The diaphragm covers contain a large spring and are under light pressure; expect it. Avoid using carb cleaner on or around the diaphragms; you're just looking for holes. Don't bother messing with the needles at this point.
Stop here; now it's time to take off the float bowls.
Open the float bowls and remove them slowly. Do not disturb the gaskets. If the gaskets are damaged or just look awful order new ones, but most seem to last a very long time. Blow air and carb cleaner through the hole and tube in the float bowl itself.
Measure the float height and record it. Remove the float pins holding the floats on; I use a punch, but you should only need very light pressure to remove them; do not force them; it should be easy. Note whether the floats are brass or rubber.
Remove the float needles and inspect them. Are there deep grooves? Remove the float needle seat and inspect the screen if it has one; clean as needed.
Remove the main jet with an appropriately sized flat head screw driver or butter knife; note the washer and remove it. Record the number printed on the main jet and which side it came from. Push the emulsion tube through the venturi (note the pin that keeps it from rotating) with something soft (i.e. not metal); plastic things work; inspect the emulsion tube, especially the tiny holes in the side of it and clean as needed. When reassembling do not over-tighten the main jet.
Remove the pilot jet cap/cover/plug if it has one. Remove the pilot jet with a very small flat-head screw driver and record the number printed on it. Once the pilot is screwed out all the way do not attempt to "dig" it out; just flip the carbs over and shake/smack them lightly with your hand and they should fall out. Inspect and clean the pilot jets including all holes in the sides. Blast air and carb cleaner through the pilot circuit. When reassembling do not over-tighten the pilot jets or the cap screw/plug/etc.
Stop here and post all the numbers you recorded. Someone, or me, can tell you if they all appear correct before you reassemble everything. Many of the numbers printed in the manuals are wrong.
Don't forget that the emulsion tube must be inserted before the diaphragms can be re-installed.
When putting the diaphragms back make sure the needles slide into the emulsion tubes; do not force them down without looking through the venturi. Make sure the diaphragm fits over its grooves properly and makes a seal; there is also a notch you need to line up. Insert the large springs and fit them onto the cover when you place it on. Do not over-tighten the cover.
This procedure is much easier than it sounds; if you're unfamiliar with the vocabulary look the words up; most carbs have all the same parts but are simply shaped different. If everything checked out with the diaphragms you will likely not have to open those covers again for a very long time. Much of the reassembly is simply the reverse of removal; I simply added tips where I deemed appropriate.
In addition to what I described there are a few more things you can clean. What comes to mind first is the idle fuel screws. You might have a tamper-resistant design I am not familiar with, but that can be removed. The tamper-resistant design has rubber o-rings that tend to disintegrate and cause problems. The older designs like my 78 have no such o-rings. Turn the screws in all the way BY HAND, stopping when any resistance is felt. Screwing these in too far can snap the tips off. You want to note how many turns were required to close them all the way; write this down. Now, remove these screws completely and clean as needed. Once done you can screw them in all the way and turn them out the same number of times that you recorded earlier. I would save this procedure for last or even skip it at first, especially if you have the tamper-resistant design. Revisit this procedure if you have problems later.
I hope this helps