I think the most common response you'll get will be pet trainers. They do provide a large amount of experience per battle but id does sound like there are things you can do to improve things.
First a handful of links for teams for pet trainers:viewtopic.php?f=10&t=4580viewtopic.php?f=10&t=4314viewtopic.php?f=10&t=7023viewtopic.php?f=10&t=7556
The older guides can still be useful. You seem to have enough pets that you shouldn't need the beginners thread.
Making sure you have good teams setup and a pet team add-on to make selecting them easy will help make things easier and it should go faster than an hour. Most of the teams should be pretty reliable and should only rarely have losses. I like rematch now but PetBattleTeams worked fine for me for a long time too.
While doing trainers there are things you can do to maximize your exp:
1. Make sure you have your buffs. Hat and 25% pet food should be the minimum. Hat 25% and 50% is great but you can only get two 50% treats per week. PvP weekly and the CT weekly. They all stack so that is a huge increase in exp when combined.
2. Work out your routine so you minimize your wasted exp. Based on your combinations of buffs there are certain points that minimize your wasted EXP and minimize the amount of leveling you have to do at 24 to finish it off. When I do my leveling of level pets from level 1 they end up a fight or two short of 25 and I don't waste any trainer exp. Unfortunately I'm pretty much out of level 1 pets to level now and am starting to work on wild pets that are random levels all over making this harder.
3. Minimize travel time. Use tomtom or some other similar add-on to make sure you are heading the right direction. Parking alts at trainers also works well. Some can be relatively low level while others will aggro stuff and need to be higher level. Alts can also maximize the benefit from the food buffs. I've got alts at all the old world trainers that give bags (deadwind pass, Winterspring and Shadowmoon) and at Aki in the vale.
You'll probably need to do the beast of fable to get the less pet treats at least occasionally but don't do it when you are using the 50% pet treat as it wastes buff time.
Yes. You are limited to a couple pets every day but it is pretty fast and provides stones for those remaining pets you still need to upgrade.
If you want to try to grind it some other way instead of or in addition to the trainers/spirits then I'd recommend the area's near some of the beasts of fables. Nitun for example has tons of critters around him and it's almost impossible to kill them all. A team with a carry pet, a strong beast with a heal (Xufu or a zlandy raptor is my choice) and a third good pet you can grind pretty much non-stop. There are tons of beast by Kafi or gorespine but mechanical pets that have heals are rarer.
I'm not quite full 25 yet but I am getting close and it is primarily from the trainers and spirits. I did do some leveling while capturing wild pets but that is a distant second at this point I'm sure.