The carrier and the front facing position can be the biggest problem. Ideally babies shouldnt be forward facing in a carrier unless in a lotus carry (using a wrap)
Some carriers are narrow at the crotch and make them tip forward rather than with thier knees higher than their hips, its not good for them and it will mean the nappy is squashed and you will likely get some gaping and compression issues.
Personally I havent had any problems with leakage in carriers (I lie..I did once but that was my bad when he was teeny tiny) and I use all varieties of nappies when I go out, pockets , AI2s and fitteds with wool. I do almost exclusively use bamboo which will help as the moisture can be squished back out as it can with microfibre.
I would suggest a two part system, either with a PUL wrap or wool (well lanolised!) certainly something bamboo with plenty enough absorbency for the amount of time its going to be on for, that should solve your problems