Zulubilly,
The existing mounting bolts are likely conventional speaker mounting bolts with a flat head that sits flush with the face of the baffle. The easiest solution would be to find an internally threaded coupling to connect the existing bolt to a new bolt you would screw in after putting the speaker in place. The trick is finding a threaded coupling that will fit through the holes in the speaker frame; there may not be adequate room for a coupling. To confirm the existing bolt threading, take one of the nuts to a hardware store and match it to a bolt that fits.
Your other option is the one you mentioned.
A third option would be to cut off the existing bolts flush with the inside face of the baffle. Drill holes for t-nuts from inside the cabinet (protect the grill cloth with a piece of scrap lumber). Reach between the baffle and grill cloth and push in the t-nuts. To seat the t-nuts, drill a hole in a piece of scrap lumber (about the thickness of the speaker rim) and screw in a new bolt through the scrap and into the t-nut and cinch it up. Then you can mount the new speakers. Of course you destroy some of the originality of the cabinet doing this.
Good Luck!
Ryan