Bigger.

That 770 wats is the steady state current, but every time you turn it on it draws a lot more for a fraction of a second. It'd be best if you could get in touch with the manufacturer and find out what the starting (or inrush) current is for your router.

You also want to make sure that your inverter power rating is for continuous output, not steady state input consumption. Because the first number is smaller than the second, the ad copy a lot of times will list the second because people will go for the bigger number.

Finally, if you can get a vehicle with a robust electrical system near by, you can take your power input from your vehicle instead of a battery. I've done that to power emergency pumps and tools (lower powered than your router).

Good luck,

Laszlo

   Laszlo is right.  The inrush will likely overload and trip out any inverter smaller than 1500 watts.  Keep in mind that on the 12VDC side, a 1500W inverter will have a nominal 12VDC draw of 125A (!).  That will mean DC conductors something like 4 gauge or bigger, which is thicker than the main battery cable connection on your car.  Rent a generator and get however long an extension cord you need, or go old school and use hand tools.  Planes, chisels, draw knives, whatever you need.  Or move the work to a place with power.

   Thanks to you both! I’ll stick with old school. 

   How big is the bit you want to use?  Ryobi makes a $70 bare tool 1/4" laminate trimmer in their One+ line of 18 V battery tools, or $129 with battery and charger.  You may be able to find something similar for a tool line you already have batteries for.  Maybe spending that kind of money for this isn't an option, but wanted to throw it out for consideration.

   I used a small round over bit in a air tool, worked ok but a little slow.

Portable generator’s probably best if you do this stuff often enough or have other uses for making the expenditure. Same goes for something like the Ryobi tool mentioned earlier, or Dewalt’s battery-driven ‘RotoZip’ equivalent. (I buy tools when I think I can make use of them again, got into Dewalt years ago so I’m stuck there now.) Best option for infrequent need is ‘old school’ hand tool(s) where possible; their utility and the skills that you learn with their use will always be handy.

Rent a generator.

or

Move the boat to power.

or

Use old school.

The Wen should do for the stated problem: running a 770W router.

As a rule of thumb, electric motors require 2x their rated amperage for a brief period during startup. The Wen you reference delivers 2,000W “surge wattage” (i.e. startup) so it should get a 1,000W motor going. It has a 13.3A rated amperage (1,450W) so it should keep that piece of equipment running just fine. The 770W router is well within these limits.

JonnyWalter, your equipment is not necessarily the same as the original poster’s. Be sure to read the data plate on your equipment carefully. Any motor at or under 1,000W should work.