Back in previous expansions (started in MoP) when I was still gathering up my collection, I would do all the satchel trainers, Beasts of Fable and MoP tamers.
Shrine of Seven Stars into jade forest, into kunlai, into townlong, into vale, into dread, into krasarang, into valley, finish off with teleportation/HS/portal roulette juggle to Uldum portal+Hyjal (winterspring) portal, fly Karazhan, Argent tournament tabard, Shattrath-Fly outland. The last 5 i can really not remember the order, but I had to use my HS twice I remember and it would come off CD, perhaps 1min wait to lineup. The last 5 didnt have same XP as MoP Tamers, nor did i carry on beasts of fable, so those 5 tamers would be used on lvl1 pets to bring to lvl 8-9, prepped for the next day against backline damage. If DMF was up, that would be done afterwards and treated like MoP Tamer XP. These 8-9 prep would rotate in on MoP tamers to get bump to 13? -> 17/18? -> 22/23 if i remember correctly. Because XP is hit with diminishing returns you would want the lower-XP giving tamers to bump as many levels as possible. Also you wouldn't want to take your level 22,93XP pets for another tamer, it wasn't effecient. Instead I let them stack in journal until I had a good handful, then take Raptor x2 and cap them manually against critters in Valley.
Satchels back then gave shitloads of blue upgrade stones and there was strong stone-upgrade trading on this site. Beast, flyver, critter was in demand naturally. This was before WoD, so you got ur safari hat and your 3x 25% xp sausages, of which you would consume 2 a day. One for the main mop-route which could be done (incl. BoF) in 55min as alliance, might have touched 50-52min once. The next sausage for remaining 25min of old world 5 tamers and DMF if up. One sausage to stack in inventory. BoF was done as it was on the route anyway and quickly with bomb-team, satchel for sausages, stones, pets->money.
With WoD release, more "MoP level XP tamers" was introduced, 6 to be exact with Ashlei being easiest and giving tad higher XP. I found Vesharr+Cymre the hardest, and with 30-35min on 2nd sausage, I decided to remove them and take the 4 others. As alliance, Garrison HS to Ashlei, fly west to Taralune, BMAH check+Tarr, finish FFR at Gargra. 2hours of all MoP tamers (normal+spirits+Beasts), 5 old world tamers, and 4x WoD.
Every day. It ran like clockwork, some days you would experience shit RNG against you, but there was enough lee-way for 2 sausages to hold the time. Back then hit accuracy % wasn't normalized, so your 95% Moth Dust, and Pump might not hit etc. Bandages you would use only a few throughout, I had my teams sorted in a way, that if I needed my pet again later, a heal button click would be inbetween. Not to waste bandages, but let those stack as well -> send to alt. And they didn't stack as high as they do today
Nightmare on alt, took a lot of space
As collection grew, they secretly nerfed the blue stones droprate, no more wild pets to capture, all breeds captured that I wanted (as rare to save on stones), the BoF was taken out of rotation. Later the 5 old world tamers as well. Then they announced Weekly XP week thing in WoD or Legion - can't remember and it basically made anything previously obsolete to a degree.
With XP pet week, you could now just with 2x MoP/WoD/DMF tamers bump your pet from level 1 to 17-18-19-i dont know, and then cap straight to 25 with second tamer. Sausages no longer needed to be used as well, wouldn't make a difference anyway and you would just waste them. Safari Hat still on as its free and looks good 8) (kidding). I could incorporate Veshhar+Cymre now, but tbh, I've been too lazy, so I don't. There is no rush as theres no foodbuff ticking, so you can slow down the pace, alt-tab, YouTube inbetween whatever it is people do. I only ever level my pets during XP week now, I have never touched Squirt, Galveston or w/e they are called, never looked into it. My needed, having already built a large collection and "being up to date" with future pet-releases didn't need repeat-XP methods. I mark my level 1s as favorite in my journal, so they get on top, and then I just slot them into carry-slot during XP week doing the Lite-version of old route which now takes less time covering both MoP+WoD. When they hit 25, remove favorite tag, and into collection they go to collect dust.
For every XP week you get 7 days to do 11+6 = 17 tamers every day, +2 on DMF overlap (I do 11+4 cause lazy). That is nearly 60 pets every event you bring from 1 to 25, being blue pets ready to go, with a Hat on. That is plenty fine if you're collection is up to date or up there in numbers. Minimum effort, maximum reward is what we try to achieve. What about backline damage, now that we use level 1 pets? Easy enough, like I wrote earlier, I start with Hyuna in Jade Forest which gives several tamers without backline damage, so for those tamers that does have backline damage, you simply slot in one of those level 17-19 pets (still cant remember exact level they land on) instead of a 1, there is plenty to go around.
If you want to optimize further, try and find strategies that are fast (less rounds needed), using variety of pets (not same again and again -> requires heal too often) and is prone to withstand a bit of RNG against you (crit against you). Restarting a fight is the biggest culprit in doing this fast. Whenever I saw odds against me, I would forfeit right away, no point in wasting time, bandage, go again, I was "on the clock" with sausage buffs back then. Never used the +50% food, couldn't incorporate it consistently in my method, so didn't bother.
Lil XT store pet was used for 2 for two tamers with similar setup (Moruk+Hyuna) having bird+beast+aquatic. Heartbroken tantrum would take total health away = two pets before dying itself which was great value. My setup was always: pet1, switch/re-switch carry, into pet2. Simply because of consistency in remembering all the strategies in your head. When first pet died, you knew automatically to switcheroo the carry into 2nd pet who would finish off the fight. Another fun thing was TCG Puffer Fish able to do some damage on Zusshi but after hit%-accuracy patch would leave the first pet at consistent 1hp - what a bummer, so had to change strategy.
TLDR: MoP+WoD+DMF tamers during XP week.