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I rode 100 miles today and the only thing that was warm at all was the contactor coil.

First off, congrats on your achievement of extending your range!!

You could eliminate the extenders contactor & instead just use a switch (just make sure it’s rated for the load & voltage @ DC).

Just a thought… maybe use a high temp wire as a resistive conductor & parallel, the existing 4’ cable? (The small gauge & long length adds resistance).
As suggested before, this would be the #1 on a rotary/cam switch (OFF-#1-#2)   
A small gauge high temp wire sized correctly could offer battery balance.
You could experiment with very light gage standard copper wire until the wire doesn’t vaporize @ the greatest Delta V (incrementally increase wire size until you find a sweet spot/size).
Or as suggested before, use an incandescent light bulb (MR-16?) as the resister.

The main thing is you produced a functional device that you can tweak out the fine details. 

So you’ve connected on the load side of the contactor at the input of the controller.

I would do what T.S. Zarathustra suggested.
Find a surplus rotary switch (OFF-ONE-TWO) & install a suitable resistor on the #1/BALANCE circuit that will allow main/extender balance. (Note that it would have be be rated for 125VDC).
It would be nice to find one that is sequential so the batteries are balanced before direct connection.
A surplus analog voltmeter installed across the two packs would let you know when it’s safe to rotate the switch to #2/RUN position

I would use a FLNR-35 or 40 amp fuse as it is a timedelay fuse with a 125vdc rating.
In the AC side of wires, #10 is limited to 30 amps so I wouldn’t feel comfortable pushing much past that & your testing shows it’s not necessary. 
AC motors have upwards of 7x inrush current to start (compared to RLA [Running Load Amps]) & these fuses are used. 

“ I am not sure how you could segregate the charge and discharge paths. The packs are just connected in parallel with a positive and negative wire. I don't see any way that diodes could solve the problem.”

The separate paths would be to add a second conductor on + or - side & install diodes on each conductor that block current in opposite direction.
This would only be required if it’s found that the extender battery cells have different charge/discharge amperage values.
If the same or close to the same, there’s no reason to do this.

Maybe ask on RC, or off grid forums or other electronics based sites how best to protect the batteries. 

That is a great idea. I don't have the expertise or knowledge to build that or answer your question. No doubt that it is possible and would solve the safety issue. The Zero power tanks do that. Maybe someone with the right skills can chime in. I did test the inrush current today with the main pack 2 volts higher than the extender and it was only a peak of 6 amps and then slowly tapered down from there. The extender is only 9% of the combined packs capacity.

I'm not sure which pack would self-discharge first. I would assume it would depend on the health of the cells and what the current draw of the BMS is, or in the case of the bike, any associated electronics that are drawing current while it's turned off.

I should add that the circuit is protected by a 60 amp fuse so there will not be hundreds of amps burning everything up. The BMS is rated at 60 amps continuous, the contactor at 50 amps continuous, the wire has an ampacity of 80 amps and the cells are rated at max 10 amps each discharge so 60 amps.  These are LG M26 cells, 2.6 ah each, 6 in Parallel.
 
There is an issue with cell balancing. My bike has the replacement BBC battery capped at 12.6 KWH. They do that by limiting the charge voltage to a bit over 115v. The extender BMS is set up to charge to 4.2 volts per cell, so 117.6v total. it will have to be fully charged off the bike occasionally to retain balance.

Fuses lag a bit in protection as they are a melt to protect device so high current passage is possible (albeit very briefly).
Time delay fuses extend this time as they allow for inrush current (as apposed to sustained).

Another idea for cross current protection is to install diode(s) to prevent back flow.
To allow on bike charging, wire it/them through the N.C. contact of a double throw contactor(s).
Figure out how to energize the bypass contactor(s) when in charge mode. The N.O. contacts would bypass the diode to allow back current for charging.

AWESOME!!!
That looks like a bit of work but hopefully this repair will last the lifetime of the bike. 

What about 45mph & 55mph?
How about 50mph on a flat road & when transitioning to an uphill grade without moving the throttle? (Obviously your speed will decrease).
I’m trying to rule out a “flat spot” on the throttle.

Is the surge speed or throttle position related.

Try asking at Energica Owners Motorcycles Group on Facebook