parallel #8 or #10 from splice point in outdoor box for 60 amp rating?
You're not allowed to parallel wires smaller than 1/0 AWG (NEC 310.10).  Further, paralleling requires special equipment on the supply-side, and special dual lugs on the load side.  This equipment handles certain very serious problems that can arise with paralleling. 

Not least, what happens if one of the two wires breaks or has a contact problem, and all the current is flowing on the other wire? 

It's maybe not so bad since since your issue here is entirely contained inside a junction box... however, it's maybe not so hard to get some #6 wire. 

If you must cheat this, use a single #8 wire and declare "inside the box" to be a 90C environment, 55A@90C rounding up to 60A. That's not legal either, but it's a better argument than paralleling.  Then do replace it as soon as you can obtain some #6. 

NFPA does a lot of thinking about electrical safety in writing the NEC.  Many rules didn't make sense when I started, but do make sense now that I have some experience and have thought more about all the reasons.  I have never found a rule that didn't make sense, both in terms of safety and finance.  

An example is the "neutral on switch loops rule" -- it causes 50 cents worth of additional hardship at install time, and saves $200 of additional hardship (or a dangerous hack) when the homeowner wants to install a light switch.