Moving Matthews inside doesn't make sense unless Martinez is hurt. They would need to play the same role in the defense the majority of the time and Martinez is better at it. Matthews isn't going to play a Burks-style hybrid LB/S role. They'd only play side by side against very specific looks or the rare offense that wants to come out in a lot of 21 personnel.
If he continues to play like he did on Sunday Night, the best thing they could do is move him to 3rd on the OLB rotation and move Perry and Gilbert up. Against the Bears, Matthews had 60 snaps, Perry had 41, and Gilbert had 37 (70 possible). That's 86%, 59%, and 53% respectively. So move Perry up into that lead role, increase Gilbert's snaps, and make Matthews the 3rd guy. Better yet, sign a competent 4th rush (Simon, Means, Ayers, someone...) and cut his snaps even further. Maybe Matthews can still provide some pass rush production if he's given limited work.