The cartridges need to take in air to replace used ink, else they will develop a vacuum and they will stop printing, so it is not a good idea to seal the vent holes/serpentine path. I'm rather sure the cartridges are leaking due to overfill.
There are different versions of instructions depending on which refill kit you buy and some instructions are more complete than others. Here is a link to an instruction that tells about overfill, see paragraph marked 2 :
http://www.inkbank.com.au/category24_1.htm
I have some old HP printers and have refilled many HP cartridges, mostly the 45, 78, 56 and 57 families of cartridges. I don't know the cartridges you refilled, but they appear similar to the HP type 56 black. I have had a 56 leaking after refill, and removing a few ml of ink stopped the leaking.
Many HP cartridges are made in a standard version and an XL version with higher capacity, so it is important to know which type you are refilling. Not all the cartridges are marked with capacity, but you can find out from HP website. If a cartridge has a rated capacity of say 15 ml, then it should be refilled with only 80% of this or 12 ml. The reason is that when the cartridge stops printing there is still some ink left in the sponge, and the 15 ml is the amount used when manufacturing the cartridge.
These opaque sponge type cartridges with built in print head are much more difficult to refill properly than the transparent Canon BCI 3/6 and PGI5/CLI8. I admit my success rate with HP cartridges is well below 50%.
Please try and remove about 2ml's of ink from both cartridges and tell if that stopped the leaking. Good luck