I concur.
I've used subs in smaller systems as mentioned but found large quality floorstander are exponentially better at achieving a clean accurate representation of wherever is being played.
Running subs seamless as people mention "as if they are not there" is rather pointless (with speakers that don't need any extra anything) which indeed brings in its own phasing issues etc.
From what I've gathered from prior comments the OP is using triangle Titus ez ?
A frequency of 55Hz to 22kHz (the lowest note on a piano is 27hz)
Lower bass being anything below 40hz.
This is an impressive number for small speakers even lower than some floorstanders.
I'm not sure what would be gained by a cheaper sub woofer trying to contend with already existing quality speakers.
It would normally bring into question the amp in which the mission 778x instantly negates.
(I demoed that amp at length and in line with the reviews heard it at being very capable)
Perhaps a quality equaliser as I bought for the opposite problem of too much bass would give you a way of elevating what your speakers are already "more" capable of.
I have a second vintage set up, the inclusive pioneer a-400 amp is without tone controls and would go that deep with QA 3050i's my jeans would vibrate making my legs itchy (no joke it would also bring things off the shelf) 😕
I've had large subs that can't replicate the inherint bass of a good lone pair of floorstanders.
The "Triangle Titus" speakers even go 3hz lower so your setup is certainly not lacking the capability to give you the vicerale bass your after.
I must admit it's been my experience that speakers with drivers below 6" are naturally never going to sound as naturally good with bass despite specs, I've never heard bass produced as good with smaller speakers bringing physics into play.
I find a sweet spot of 8" with floorstanders but that's personal preference, many with true 6" drivers can move enough air to land the police at your door.
I bought a quality equaliser (Bellari EQ 570) that does not negatively impinge on the signal which has a complete tear down review-
https://community.klipsch.com/index.php?/topic/203557-bellari-eq570-analog-eq-measurements/
And further flying reviews
Oh wow!! I just got the EQ570 a few minutes ago, and currently listening to music through it as I type this. I have goosebumps. My home office stereo system has been bugging me for years now—it doesn’t have the same uumph! factor as my main system. It lacks liveliness, and not as engaging...
audiosciencereview.com
I can say personally it's a good little solution for enhancing an (already existing) frequency response.
Maybe modifying what your system is already capable of.
But then again maybe like me when you get and itch to scratch your best off just scratching it and trying a sub woofer.
One of the best budget sub woofers I've heard is the "wharfdale SW-150".
I demoed a few in that category whilst looking for a sub to cover movie SFX in a second hifi.
A true champion of subwoofers, in terms of performance and price – it’s a quality piece of budget equipment
www.whathifi.com
It runs clean and powerful bass without sounding muddy.
I admit it remains off for most of the time as the floorstanders make it completely pointless but for movies it's good.
Despite going up a few notches for my main hifi and after many demoes at RS then purchasing a bigger and better sub woofer it also now after changing to large fyne audio floorstanders remains off.
Just a thought 💭