I believe bypass and sidestream are referring to the same idea, which is that, rather than putting the filter inline with a system supply or return, you put it in a "sidestream", i.e. a parallel piping path to the main system path, and divert some flow through it using, say, a partially closed ball valve or other flow restriction. Since there will be a small flow through the filter whenever the system is running, over time all the system water should get filtered (at least in theory). In any case, the idea is to keep the filter out of the main line so that even if the filter isn't maintained/cleaned, it won't begin to interfere with the proper functioning of the system. Sidestream is also relatively easy to retrofit, you can cut it in pretty much anywhere.
According my conversations with Chris Holley, a dedicated mixing loop is also an ideal location for a filtering setup, since it also won't interfere critically with the heating system's functioning if it becomes clogged, etc. If you pump say 15gpm, you should get all 1830 gallons in about 2 hours. So two passes per firing, sounds fine.
There are several options for filter types. For a sidestream type, Chris suggested a stainless canister + spun cartridge filter, 5 micron. The Dirtcal is a Caleffi product, it is a vortex type separator (doesn't use a filter media, creates low velocity vortex which drops the dirt to a chamber in the bottom). The Dirtmag is a version with a magnetic separator which is good if you have ECM circs. My understanding (please correct me if I'm wrong) is that these vortex-type separators don't work as well with a very low flow rate, so might be less ideal for a sidestream type setup, and more ideal for a inline mixing loop application. I have a 1" NPT Dirtcal which they spec for an optimal max flow rate of 9.3gpm. If you go up to a 1-1/4", that is 15.3gpm. In my experience with the Alpha pumping 13gpm, it is enough to provide good mixing for the Garn (although it still doesn't disturb the topmost layer above the supply tapping).
One idea that just occurred to me is, if you pump from the bottom to the top, you could drop straight into the top of the tank and just let it splash down. Not sure how this would work, pumping an open loop like that, you'd probably need a foot valve at the intake end to keep the pump primed. And I don't know if the regular wet rotor circs can do that, esp. with 190 degree water they might cavitate running them in suction like that. The advantage would be that you'd be mixing into the very top of the water level regardless of the tank temperature (the level goes up and down probably about 3" from 120F - 190F).