Dale,
No doubt the sound is available with your rig. Sure, I'd try different strings first, but before trying that, I would adjust EQ controls- try on the bass and on the F1-X.
One thing I find is that your home stereo, car stereo, bass rig, etc. only sound as good as your speakers. In other words, you could run an F1-X and World 2.1 through an open back single 12 guitar speaker and the sound would be horrible. You could run a 3rd world heap of an amp through a Bergantino HT322 and get some good useable tones.
The SWR speakers are great, but if you can't get satisfaction from changing strings, take your bass and amp to your local music shop and listen to other speakers, like the vintage series by Bergantino- they are built without tweeters and are designed to provide a good low end wallop-very vintage, fat tones. I definately recommend you try no speaker with a driver smaller than 12 inches. A good 15 inch box or two should help to move some earth.
Keep in mind you can affect your sound by adjusting your set-up, but if changing it too much hurts your playing, then trying a different speaker box may do the trick.
Personally, I used to use a Stewart amp, and switched to a Mackie M1400i. Is there a difference? Goodness yes! The Stewart seemed more hifi, and the Mackie is way F A T , very thick and bassy. Another box to try if you can find one is the Acme B2 or B4. Great sound, but maybe a bit too refined for your taste- more modern sounding than the Bergantino Vintage Series boxes.
A great vintage tone on your bass (as I have found on my short scale SC Deluxe) is to favor the neck pickup- leave just a tad of bridge pickup, roll the treble off on the neck pickup filter about 1/2 or so until you get a totally convincing '62 P-Bass sound. Heck- that may do the trick altogether!
I've been where you are- and I've spent thousands on a bunch of speaker types, as well as make my own. I've settled on Bag End speakers. Through the years I've bought and then sold them, only to find that they are the most musical sounding (very smooth tweeter, smooth low to mid to high tones).
Start with tone tweaking, and if you can't get the sound, start checking other avenues, the lowest cost and up from there.
Good luck!
Alemboid