GPS data on all commercial devices will be short in the woods.  Too many quick switch backs and satellites don't have clear line of sight.  That is why Garmin's support a wheel sensor, which overrides the distance.  You will not get accurate distance without a wheel sensor.  I believe some phones may be able to pair with sensors, but I haven't tried it.

The reading it gives me over the main and lake loops at Sherman is 295 feet.  I'm not sure what the actual is but that doesn't seem far off just by my gut feeling.

Strava is hit or miss on my phone. 

On Average when I do all of Sherman I finish with 10.4mi to 10.8mi

but a few times I've finished the full trail with a read out of 9mi to 9.6mi

So depending on how fast you go,if the weather is clear, the canopy is clear and if the planets are aligned, you may get varied results. 

Website says Sherman is 11.6 miles, Kiosk reads only 11mi. so getting 10.4,.6,.8 mi I will attribute to not having a speed sensor and just relying on the GPS

It is a cool way, but requires some additional investment.  No such thing as a free lunch.

I have not run into the issue where elevation is ignored on subsequent laps.  It works fine for my garmin device.  It's not really strava that is involved if you are using a device.  Strava reads the device data.  It does some smoothing and correction on the data, but it's still relying on the device for it's input.

Strava segment matching is a tricky one for me.  GPS drift, poorly designed segments, and trail changes can make them unreliable to match.  It just happens some times.  You can see how much drift you are getting sometimes if you do multiple laps.  You want them to be very close to each other, but sometimes they can be pretty far off.