Lack of bass

[yogo]

The original woofer was designed or chosen to work in that cabinet size.

Every speaker has certain characteristics. These characteristics have to be accounted for when building a speaker system. You can't just throw any speaker in a cabinet and expect it to work correctly.

What you have is a closed box air suspension speaker system. The speaker you have installed may be made to be in a ported system as opposed to an air suspension system.

If it is an air suspension speaker there may be not enough air in that size box to allow the new woofer to move enough in the lower frequencies to produce low bass. That may be why you are missing bass as the freq's get lower. Many other factors such as impedance may also contribute to poor sound such as an imbalance volume level with the tweeter.

I would buy an original replacement speaker or replace the surrounds on the old pair of woofers.
There are surround kits out there for like 25 bucks. I did my Baby Advents and it was an easy job.

Unless you're a speaker designer I wouldn't try to redesign any already optimized speaker. You'll be wasting your time...