Is there a way use an RDP to configure a continuous offset from GPS calculations? Is there any way to configure a location offset in such a way that my phone's GPS data would still be used to set a location, but an adjustment value would be applied to the base value? (e.g. all values adjusted 6.5m SW). Two cases where this would be useful are when using programs that have base maps with bogus offset data, but you want your phone to think it's in the right place on top of the bogus data. Also, sometimes the coordinates calculated from the GPS system on a given day are just simply wrong, and usually on a given day they are wrong by a fairly fixed amount. Rather that spending the entire day with my phone marking me 30m north of where I actually am, I'd like to correct the values automatically based on a known RDP location.

Ideally I would like a way to 'zero' my GPS by calculating an offset based on my current location being a set of known coordinates, then allow the GPS to adjust my location based on that. I would enter "I am currently at X", at which point it would figure out that number is 4 meters off of the GPS readout, and thereafter sets my location to be always 4m offset.

I realize there are lots of programs to set a mock location of my choice and even ones to follow recorded routes. These sort of things that entirely replace the output of the GPS with fixed or otherwise pre-programmed output are not what I'm looking for here. If it matters, my devices are all rooted and running CyanogenMod 11 M2 so root only solutions are acceptable, although if there is a non root way to do this that would be good to note.
Those offsets are normally used in differential gps. A fix point (station) knows it exact location (from manual measurments), calculates from the gps data the requred offset for correction and send this (quasi constant) offset (ex. 2.5m SW) to you.
The  assumption is that if you are close to this station the atomospheric error (=offset) is valid also for your position in some distance.

Im not too familiar with android, but you could send manipulated D-GPS data maybe?

For radio those are send with RTCM (Radio Technical Commission for Maritime Services), (you can get down to 2cm accuracy) - for mobile phones you need to stitch to Ntrip (Networked Transport of RTCM via Internet Protocol): http://www.rtcm-ntrip.org/home most of them are non free/paid, so you need to look around (if you really want there a ways to make your own low cost server (raspberry pi..))

would you still need offset if the accuracy is already very good? Boosting accuracy seems easier!

Have a look at https://play.google.com/store/apps/details?id=com.lefebure.ntripclient
==> ACCESS_MOCK_LOCATION - Used for routing external position data to other applications. but this solution has also it downsides :-(