Hi Andy, I have bought 2 of those bridges, a fiver and 4 banger, only to find the saddles at lowest height sit higher than most F styles and reckon that is where a lot of the high action problem is coming from. Not sure I would risk routing as it would need to be very precise to help counter sink the whole bridge base plate which looks to be a couple of mm thick. I am in a similar predicament on my EX-5 and look like re-installing original kit bridge as it has more up & down saddle height adjustment available. Plenty of really, really expensive ones out there that might do the job but not prepared to spend over $100 bucks for minimal gain, if any at all. I have used one of the better quality ones as a replacement on my J Bass and only similar one in black is a Gotoh for $75.
If you are tempted to drop in a Riccy look-a-like Real Parts sells them for $99 but currently out of stock. Couple of recent RC4 builds using that style show that routing is required but with a bigger baseplate many mistakes can be hidden. They only come in silver/chrome.
At the Nut, fret at 2nd and the 3rd frets to see how much gap above string at 1st fret and if more than business card thickness things need to be lowered at the nut end too. Brass is very hard if you need to file or sand it down to lower the action and takes forever which tends to make bone look like the better alternative.