i use soil blocks successfully. my mix is like yours but i use a bucket of top soil or potting mix and 1 bucket of peat. i don't always use compost. depends on whats available. i compress the blocks a lot when i make them and they stay together very well. i use a soft spray to water them.
you have some pictures of your blocks?

I use coir instead of peat and get better results with the coir.

Are you starting smaller seeds in the 1" mini-blocks?

I use permanest trays under the flats the blocks are in so I can bottom water. You cannot top water soil blocks without them melting so get them on trays of some sort and bottom water

I had wondered about the coir because I heard it was a better planting medium. I may have to try that and see if I get better results.

I don't have that much of a problem with them holding their shape. I don't think I have an up close picture of them in action. I do bottom water but it seems the ones in the center don't get as much water. I recently bought a soft spray nozzle that waters them pretty well without melting the blocks, but I've only had it about a week.

My biggest concern was the soil mix and the fact that the seedlings don't seem to thrive in the blocks. That's why I was curious if I was doing something wrong. Do you fertilize your blocks? How wet should the blocks be? I also notice that I get quite a lot of moss/white fungus on the blocks compared to the trays. Could that be an issue as well?

Thanks for your help!

It sounds like you have a contamination problem as there should be no white mold on the blocks. I would suspect the peat as the vector, though it could be anything such as the flats.

if you can afford it consider getting OxyDate. We got some this year and it has stopped the damping off we were getting with our soil blocks (a problem that got worse each year until Oxydate and getting the flats really sanitized). Cinnamon can also help.

As for the center blocks not getting wet use more water so the blocks are literally floating in their tray and let them stay in that water until fully hydrated, which can take up to a half hour iof the peat based blocks have dried out completely as peat is hydrophobic (doesn't want to absorb water). Coir, on the other hand, is hydrophillic (loves water) and thus absorbs it MUCH better.

The one thing we do get with coir blocks is more algae on the tops than with peat but in the 3 years we have been using coir this doesn't seem to do much, if any harm to the seedlings.

The only fertilization we do is a weak kelp solution at the start to speed germination and than again at 3 week (if not already transplanted) if things are looking yellow.

I don't know if the plants not thriving is so much being in soil blocks, but not getting enough nutrients. Maybe just water with some fertilizer water. I do that even when using pots.

The damping off shouldn't have been from the flats. I ordered a new case and pulled them straight from the box when I was making the blocks. Should I have sterilized those as well? I was thinking it was from the compost.

I wasn't watering like you described initially and I think that was causing problems. I only recently started flooding the flats to really get the inner blocks wet.

I didn't think I needed to fertilize since the mix has fertilizer in it. I think I may start doing the kelp fertilizer to see if it helps give the ones that are having problems a boost.

I was planning to play with them a little throughout the summer when I am not on such a time crunch to get seedlings ready.

The mix's fertilizer will only last so long, alittle each week or so, very diluted will help.

Can you move the center blocks to the outside occasionally? either that you use narrower trays? Myself, I use ribbed trays to keep the center ones more evenly watered (for me, the cells get too wet in center, I haven't tried soil blocks, since I sell my plants in cells or pots.)

Peat, if it dries out, is like shredded plastic. It is very hard to get it wet again.

Try coir or something else fibrous.