GFCI and other concerns for 1500 foot wiring run
There are two huge areas of challenge for this job.  #1 the legal way to transit the pond, and I am 100% sure that laying the pipe atop the pond bottom is not allowed, because pipe is not allowed to "leap" underwater valleys as it will have no support. It will also snag any foot traffic.  #2 the GFCI capacitance problem as you discuss. 

You're also talking quite a staggering sum, even with your shortcutting lowball plan. As such, what keeps hitting my brain really hard is "Revisit Solar".   Because the kind of money you'll spend on the wire alone will buy a lot of solar. 

The barn system, sounds like it needs to be enlarged or aging batteries replaced.  

As for the gate, the need there is not so bad. On one hand, the gate motor - which pulls hard, but only for a few instants.  Because of that, the average draw over 5 days is probably less than a watt, and that's what you have to size the battery and panel for. It would really help if  you could get a 12V or 24V version of that gate.

I gather the other load out there would be post lights. I would go entirely 12/24V LED for this, and abandon the idea of having the lights burn all night, instead make it only seem that way by strategically placing motion sensors so anyone who approaches finds it on.  12/24V motion sensors exist and are in fact cheaper than 120V sensors.  Run 18/3 thermostat cable to them and have them light the light through a relay. 

Figure 2 watts average for the gate and 1 watt average for a motion sensor light+sensors, = 3 watts x 10 days reserve = 720 Watt Hours or 60 amp-hours.  Very achievable. Put 100W of solar panel on that, aimed straight vertical so snow doesn't stick to it, and if that deosn't suffice add another panel.