If the handling is likely to cause more stress and damage, then you might look into salting the system. This will knock back strawberries but most other veggies will survive up to 3 ppt of salt. Do some research to find out what salt level would be safe for all the fish and then calculate the amount of salt you would need to add to the system to get to that level. Don't use table salt or iodized salt. The cheapest bag of pool or water softener salt will likely be a bit overkill but it won't go bad and you can save it for the next "bigger system" I guess. Totally dissolve salt before adding it to a fish tank.
Here is a blog post with some numbers salt for fish health
Half a pound of salt isn't that much really. It will depend on how coarse it is of course as to how much a cup would weigh but one type I used a quart yogurt container held about 2.5 lb.
Now if you convert to grams and liters it becomes easier to figure out how much it takes to give 1 ppt.
Now this is something I don't have much experience doing. I would really recommend doing an internet search to find out what salt level koi keepers recommend for a salt dip for Koi. How many ppt of salt and for how long.
Essentially a salt dip is a fairly high concentration of salt that you really only momentarily dip the fish in for like a matter of seconds or 30 seconds to a minute, keep em in the net as you will probably be hovering right there to return em to the tank at the first sign of tipping over.
A salt bath is something you might do at a lower salt concentration but still higher than what the fish could live in. You need lots of aeration in the tank or bucket used for the salt bath. You can't leave the fish unattended in a salt bath even though the concentration is lower since as soon as the fish looses equilibrium (starts tipping over) you know it's been too long and they need back into fresh water. Salt baths could be anything longer than a minute to perhaps 15, 20, 30 minutes long but I would have to do a search on the internet to find out what they recommend for treating koi.
Well adding aquarium medications may or may not kill the plants but if you use aquarium medications not designed for human consumption your probably won't get to eat the strawberries. Some aquarium medications are pretty terrible toxic carcinogenic substances so do some homework before using them in a food system. Also, most aquarium medications can kill off your bio-filters so read up on that too.
I would suggest moving the stawberries off the system and treating with salt. Make sure the water is warm (like the link above says for treating ick.) Salt will also help most fungus. Now my understanding of Ick is that you want a fairly sudden shift of at least 3 ppt in salt level to be most effective and keep it at that level for 2 or three weeks. Move the strawberries to a fishless set up for a month and I believe any ick will die off with them because it can only survive for so long without a fish host.
Oh and I wouldn't worry too much about adding the salt suddenly causing a temporary nitrite spike seeing as having the water salted will help protect the fish from the danger of a temporary nitrite spike. Just make sure there is lots of aeration because salt will somewhat decrease the amount of dissolved oxygen the water can hold as will increasing the temperature to help shorten the treatment time for ick.