OK, after looking at your drawing I understand the reason for the confusion. I was assuming that the aquarium water would rise up far enough that it was past the funnel and into the tubing (it's hard to see from the pictures). Obviously this would depend upon the height of the funnel and how far the drop checker was submerged. You are absolutely correct that using a funnel would increase the surface area and decrease the reaction time provided the interface between the trapped air and the tank water was within the funnel as opposed to farther up into the tubing. I apologize for not making my explanation more clear, and sorry if I caused a lot of confusion. Next time I'll try and figure out how to draw picture and include it in the post (worth a thousand words).
I also thought of how to utilize a fat, and hopefully short jar even if it has a large mouth. Provided the jar has a plastic lid that seals well, you could drill a hole the proper size for the tubing (a spade bit works well for this). With a plastic lid and plastic tubing, super glue makes a quick, convenient sealant. I use it for air tubing all the time and never had a leak. If the jar/bottle is too tall, you could try melting candle wax or paraffin and using it to fill the jar part way to decrease the volume of air it would hold. I don't think it would react with or absorb any CO2 (paraffin is used for home made jams and jellies and doesn't affect the taste).