I would have thought a carbon tank would be stronger than the plastic one it has at the minute.

Strength can mean multiple things. Carbon is actually quite brittle, and failure is complete. So there's no deformation or buckling like a plastic tank would. 

I've seen (never used) rubber bladders for motorcycles. That might be an option if the coatings/epoxy doesn't hold up.  As for the carbon breaking in an accident, would a layer or 2 of kevlar on the inside hold up/ keep the carbon from puncturing the bladder?  FWIW, Most bike accidents I've seen, the person got thrown  clear of the bike.

I made a carbon tank for one of our race bikes and managed to get the weight down to 550 grams complete with cap. the tank below is made from pre preg and I made a 3 piece mould. I also used the Caswell tank sealer on this particular tank with no issues.

https://www.aircraftspruce.ca/pages/cs/fueltanksealants/ps890.php  > look in t Q&A section also > https://www.aircraftspruce.ca/catalog/pdf/09-38560-TechData.pdf

I use a phenol novolac sealer which is from a UK based company and is apparently a higher Phenol Novolac content than most which have been blended to reduce some of the costs. I am not sure how much there is in Caswell tank sealer but it is more expensive than I pay as I go straight to the supplier who makes blended resins.  The trouble with pour and slosh coating is both wastage and possibly having the sealer slump and not fully coat the inside. I paint mine onto the inner sections before I bond them together and I use an adhesive I make which is based on the same resin. This allows me to alter the resin with thickeners and additives to make the adhesive or sealer work how I want. It is not a cheap resin to buy but I would say I can do 3 fuel tanks with 1.25Kg (resin and catalyst total weight). So it is not too bad when you look at it per tank. If you are doing them to sell then obviously you would be buying 5 or 10Kg so would get a better price too.