Looking for suggestions for using a home theater without a subwoofer

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I'm thinking of removing the subwoofer from my home theater, at least for the foreseeable future.  It's a 15 year old Polk Audio that I got with a home theater bundle back then.  Since, the receiver has been changed a few times (I'm using an 2 year old Onkyo purchased a few months ago; it supports Atmos and such, although I don't have the speaker for it).

 

The bass has always been more noisy than that 'useful' (if that makes sense), at least to my ear.  Also, living in an apartment I've had to keep it down so I don't think I have ever gotten the true effect.

 

So I would like to eliminate the subwoofer and compensate with better speakers.

 

I have a 5.1 setup, with matching Polk Audio speakers (all from the same 15 year old bundle).  While I would like to replace them all, the budget right now is good only for two or three (if I can sneak a center channel in).

I'm looking at this: Polk Audio RTIA1 125-Watt Bookshelf Speakers - Black - Pair

 

Is there anything I should look out for with bookshelf speakers that may help compensate for the lack of a subwoofer?  
Any suggestions on how I could configure my system and sub to provide better bass that might not annoy the neighbors (old building, wood construction, the subwoofer sits on a foam pad and is forward firing, next to a fireplace and toward the couch).

 

Thanks for your feedback!