If you want to use previously damaged tyres then will have to accept that you must do some prework. Ordinary tyre patches should work just fine on punctures from things like thorns. Bigger holes MAY seal with a tyre patch, but are probably best fixed with a plug of some kind. There are various sorts around, let YouTube be your friend.
Using a stronger glue is your choice and it won't do any harm. I have never found it necessary and I would not bother.
Once you have prepared the tyre, including removing the residue of previous tyre sealant from the bead of the tyre and from the little trough on the rim where the bead fits. I am normally not too scrupulous about the latter, but you seem to be having trouble, so I'd just do it.
Then whatever sealant you use, give it a really good shake beforehand. Shake hard enough and for long enough that the residue at the bottom of the bottle is removed. That residue is mostly the tiny fibres that block the holes in your tyre. If they are not in suspension in the latex-like fluid, then the fluid just leaks out without sealing the tyre. I tip the designated amount of sealant into the tyre before pushing the last part of the bead into the rim bed. Then the inflation.
You need to get the air into the tyre as fast as possible. It needs a high volume of low pressure air to blast the tyre onto the rim. Lubricating the rim with some soapy water will help to reduce the air pressure required to force the tyre bead across the rim and into place. A good squirt of washing up liquid into a cup of water and foaming up with a small brush and then liberally applied will do the trick.
If you have Presta** valves, remove the valve core before attempting to inflate the tyre. This will allow more air into the tyre. Keep pumping (or allowing long enough) for the tyre bead to drop into the rim. When the bead drops inot place it is usually accompanied by a loud crack or bang and probably two or more.
Note**. This may also apply to Schrader valves, I have never had any, so I can't be sure.
Then you have to get the valve core back into the Presta without losing too much air pressure! Yes I know that it's a faff, but unless you convert to high flow valves then you are stuck with it. (Google the alternatives). Pump the tyres up to 40psi or threabouts and shake the wheel vigorously to distribute the sealant all around the inside of the tyre carcass. I then leave the wheel horizontally on a bucket or plant pot for half an hour, to see if the pressure is holding. If it does, you're good to go and you can deflate to your target pressure. If it hasn't, then restore to 40psi and do the shake and position the other way up on the bucket. Repeat.
Finally, I will no longer attempt to install a new tyre tubeless onto a wheelrim, without some sort of pressurised assistance. The airlines you find on garage forecourts are useless because the flow rate is too low. I use an "Airshot tubelss inflator", one of the best value for money devices in the industry. There are others; Google "device for inflating tubeless tyres".
Going tubeless may seem an all round faff that you can do without, but it is one of the best things I have done on my bike. When you see someone doing it who knows what they are doing it looks easy. But watching someone do it for the first time can be painful. But it does not take long at all to get success! Stick with it!
