I have been having this same problem. I had my 3 tiny froglets in a very small tank that I lined with paper towels, that I would change and dampen frequently, and removed the plexiglass top for a netting. I would drop the pinhead crickets directly into the tank and if the froglets were at the bottom they'd grab them and eat immediately, but if they weren't at the bottom or if they were full, several were always running around the bottom. I would check the tank daily and the crickets were disappearing so I'd add more. Since I replaced the plexiglass top with netting I'd have to mist more frequently and without the papertowel bottom they were constantly drowning, but when I would change the pt I'd find the crickets under the pt, half had died. It was making me nuts, so I made some changes.
In the small tank I kept the papertowel bottom for the frogs, but put the crickets in a lid from a brownie, it's plastic, see through 3" dia and about 1" deep. I lined it with a dry pt and put in several bunny food pellets I would dampen, so they would puff up, before putting them in with the crickets, this way they'd have food saturated with water so they could survive for several days at a time in the little container. Then when I sprayed the tank and try to avoid the container, but if any got in it, it would be absorbed by the dry paper towel, if any crickets did manage to get under the pt in the small container I could see them through the clear sides, but at least I didn't have to rip apart the entire tank, and they weren't drowning every time I'd spritz the frog tank.
I'd also constantly have fruit flies in the tank so they could eat any time in between crickets, they still eat both, but it was a very small tank and I had a plexiglass top. When I changed tops I'd put on a paper towel to keep the fruit flies in, but the frogs ate them up fairly quickly.
Yesterday I finally set up the 10 gal tank for them and had to change everything. Instead of pt I have soil and because of the size difference, soil, live plants and water bowel, I can not leave the ff in there or the frogs may never find them or they will drown in the water. In the small tank, when I had a water dish, the ff's would gravitate to the water and pactically the entire group would drown, so I had to take it out and make sure the pt was damp enough for the frogs and mist the pt only or the ff's will also drown in any droplets(on the sides or plant leaves). I have the same cricket container and set up in this tank too, but I have to take them out and put them in another container every few days, depending on how many crickets they are eating and how they are looking, to feed them their ff too.
It's not easy when their food is so small, but this system has been working very well for me so far. My frogs are thriving and very few crickets and or fruit flies are dying or drowning while waiting to be eaten!LOL
Hope this helps, let me know how it works for you.