Popps, while I think a swap pet option is a good idea, however, it only helps in certain scenarios and may require some thought to prevent abuse.
Scenario 1
In the extreme, imagine a scenario where I have 5 frenzies out and all my stable slots are filled with pets that takes more than 1 slot. It could happen - tamer stabled all his pets but did not realize that he had reached the limit. He then tamed/received/bought 5 frenzies, and didn't play that char for a week. All were ready to be bonded when he logs in a week later. I guess that's similar to what happened to you.
In the above scenario, if I swap 1 of the frenzies for a stabled Cu, I would have 4 frenzies and 1 Cu out (8 control slots worth of pets). If I swapped 4 frenzies for the stabled Cu, I would have 17 stabled pets instead of my 14 pet limit.
Although mine is an extreme, both your situation and my scenario is similar as both of us have more pets than stable slots due to the 5 control slots we have.
Solution 1
To prevent abuse, the logical solution would be to build in checks to allow the swap only if the pet you swap in will grant enough available control slots for the pet you want to swap out. However, what if the tamer in my scenario then makes a post to ask the devs for a solution that doesn't require breaking the bond to his 5 frenzies?
Solution 2
A solution to nip the problem in the bud for both scenarios is to block taming/transfer attempts once tamers have reached their stable capacity. But then, crafters with 5 packies (or 2 packies plus a beetle) would have a problem.
At the moment, most tamers have found ingenious ways to overcome this issue during their own gameplay.
Follow their advice - you will have to release the pet in your house or transfer it to another tamer to free up your control slots and do housekeeping on your pets. The bonding will break of course, but if you can live without stabling the pet for 7+ days and waiting for it to bond the first time, this shouldn't be a problem for you.
If you go the "releasing animal at home" route, note that even released aggressive pets do not give you the "You anger the creature" when you re-tame it, so no extra worries for those dragons/mares types of pets. They also take several hours (at least 2+ if there are no mobs outside the house that aggros them, much longer if there are. Also means that you can aggro them to extend the time, I'd once had released pets stay for days) to dissappear, you have plenty of time to housekeep.
What works for me:
1) Make a habit of feeding and stabling any new pets you tamed. This will allow you to check if your stables are full. Besides, if the pet is worth keeping, you don't want exposed to unwanted danger/training accidents before bonding. The feeding will ensure that I have made the first feed attempt. Don't want to unstable them a week later and find out that I'd not fed them when I first stabled them and have to wait 1 more week.
2) Keep animal lore at 110 real and lock it, but eat a 120 scroll. At 110 lore, you can lore all monsters, however 120 doesn't give any significant bonus other than a extra stable slot. If you find that your stables are full, simply equip an "Ancient Farmer Kasa" (it's a TOT mini arty) plus the "Birds of Britannia" totem (library collection reward). Each will grant you +5 lore, boosting your lore to 120 and giving you that extra stable slot.
3) Carrying it 1 step further, you can leave taming at 115, so the +5 taming from the totem will boost it to 120, giving you a futher pet slot.
4) I leave these 2 items at home to be shared by the 6 different tamers between my wife and myself. Will only use them to boost stable slots or when I go tame GDs/Cus etc.
5) Carrying it even further, I guess you can even leave taming at 100 and use a +15 taming jewel to boost it to 115 only when using GDs/Cus. But you need to remember to re-equip the jewel if you die and get rezzed. They are a bit onery when you have only GM taming/elder lore. For other pets like rune beetles/mares/bakes/frenzies that can be effectively controlled with only GM taming/elder lore, you can equip a different jewel for flexibility.
Hope that helps.
p/s Asking for an improvement is perfectly fine. However, this is not going to take effect immediately even if they decide to do it. Being too pushy about it tends to puts people off...So I suggest that you use the alternate methods suggested first. And use methods like keeping lore at 110 to help you avoid the problem in the interim.