I just got an email with the new 2021 sig catalog.

The suppressor section looks interesting.
The resolution sucks so the font is extremely difficult to read, but some of the highlights (IMO) are:

5.3 inch long .308 suppressor that weighs 8.8 ounces
same as above with QD - 10.7 ounces

7.5 inch .308 - 12 ounces
(no weight given for the QD variant)

Looks like they're going with an OSS style flow-thru design now to reduce blowback.

That short suppressor will not do much to mitigate blast from 7.62/.308, especially if you go shorter than 18". Maybe consider just putting a Noveske K7 blast diverter on your gun and save the $200 and the paperwork wait.
I've got a Rugged Surge full length on a Ruger Precision bolt gun and a Gemtech Quicksand on a Windham AR-10 and they both do very well. All centerfire cans sound noisy to me unless I'm shooting subsonic Blackout or 9mm subs but people next to me say the 7.62 setups are very quiet to them.

I dunno...
I have a couple 5.56 SBRs (10 inches).
A k-can on those really takes the bite off the blast.
Hearing safe without ear protection? absolutely not.
But it REALLY dials them down to something bearable.

I would expect a shorty 5.3" can to do roughly the same for .308
The longer one is more in-line with the SiCo Omega as far as length/weight goes.