As has been said, thick (toothpaste consistency) is considered healthy. I don't think it's abnormal for you to be getting thick output this soon after surgery - mine took only a few days to settle down and stop being water with my last surgery, and with my original surgery, I didn't get any output for quite a few days due to ileus, but when the output did start coming, again, it was thick in a matter of days.
Some people seem to find thick output easier to manage - it's less likely to leak by seeping under the bag - but I prefer it watery, because watery output doesn't stick to the bag opening when you empty it. My output usually is thick, I know there are some foods that are supposed to make it watery, and others that thicken it, but I haven't attempted to make it more watery since I've been told thicker is healthier. I haven't noticed any correlation between my diet and output thickness anyway. Sometimes my output is watery - maybe for a day or two every couple of weeks - but it doesn't seem to relate to what I've eaten. The only food/output correlation I've found is between fibrous foods that don't break down and solid pieces in the output.
I also agree with the above posts - you deserve having a stoma nurse to try and stop this problem! Thick output shouldn't make a bag come off.
In the mean time:
I measured my Stoma and its measures an inch the convetec pouch's I want to use are way to big for me there's to much room between the stoma and the opening which means Ill probably have more leaks.
Can you get any mouldable rings or paste to fill the room round the stoma to stop leaks? Though presumably by the time you've ordered that, you should also have been able to order some different bags that fit. I do all my own cutting - or at least I used to, since my right hand is still recovering from paralysis my dad has been cutting them. But my cutting is far from perfect, but doesn't seem to result in leaks if I cut them a bit bigger than the stoma. As long as I use a convex bag I don't get many leaks. I also find the convex ones much easier to put on correctly. Are you using them because they're supposed to be better at holding heavy output? I didn't know they could be used for that but I can see it might make sense.
Are you on any medications that could thicken output? Obviously there are anti-diarrhoea ones which would slow the bowel down and so thicken output and I'm assuming you're not taking any of those; opiate painkillers could also thicken it but if I remember correctly, you're not taking those either. But you may want to check the side-effects list of any meds you are taking, and check whether they can cause constipation.