You could do the joint by means of a "Mirror Cut" with the tools you have, but you would still need a long " straight" edge....
The straight edge doesn't necessarily need to be perfectly straight, as long as it doesn't bend more than a mm or 2.
A length of edged kitchen plinth would suffice at a push. You would also need to find a way to firmly clamp the straight edge in position at each end as well as in the centre to prevent deflection during the cut.The additional central clamping/support is a must....
The 2 pieces of worktop will need to be clamped flat to a large flat sacrificial surface with a gap between them. The size of the gap will depend on the diameter of the router cutter you intend to use.
You stated you already have a normal kitchen worktop jig, so I'm assuming you have 12.7mm diameter cutters....?
If you use this size cutter, I would suggest leaving a gap of 10mm between the 2 worktops.
Set up your straight edge in such a way as to allow the router cutter to run right down the centre of the gap. Obviously, you will then be taking off 1.35mm from each edge of the 2 worktops at the same time.
If there is a slight bend in your straight edge, the bend will be mirrored in the opposing worktop edge but when the joint is brought together there will be no gap.
Make sure you keep the router snug up against the straight edge and make sure the router cutter is good & sharp.