Changing swing check valve for a Double Check Valve Backflow Preventer
Since you are providing access to the backflow preventer...
Since you are providing an irrigation box for the backflow preventer, which means that you can access the preventer down the road, your plan is sound as far as that goes.  Note that Double Check Valve assemblies are considered testable, which means that in many jurisdictions, you will need to test them on a regular basis (such as yearly, or every other year, as discussed in this City of Tallahassee document) as well as at the time of installation.  This test is usually performed by a plumber, but your water utility may provide this service to residential customers for a small additional fee on your water bill.  This all is atop having to register your preventer with the water utility, which consists mostly of filling out and sending them the appropriate form.  Of course, if you're on a well, then you don't have utility regs to worry about, but you should still test the preventer on a regular basis to ensure that your well doesn't get contaminated by backflow.
...but as to that head loss
According to the FEBCO LF850 specsheet, a 3/4&quot; LF850 will have about 5-6psi of head loss across it for flow rates below 20gpm.  Considering that most folks won't push more than 12gpm through a 3/4&quot; line anyway, you might be able to get away with it, depending on how much head loss is in the rest of the system and what this is protecting.  If that 5psi of loss is excessive, then you'll need a booster pump after the preventer.  Note that that may impose more stringent testing requirements on your backflow preventer.