Overdrive can’t be linearized like CB can because it is an RGB “rip”. It really isn’t even an actual rip because it still uses the Epson driver, or at least the Epson media/paper settings for ink loading, how the RGB is internally converted to the CcMmYKkk ink channels in the 3880. I also use a 3880 ad have been since a week or 2 after it went on sale, guess that must be at least 2-3 years or something.
Getting back to your queries, it isnt possible to linearize a “non-native” device. By that I mean that the values going into the printer are not the same as those which the printer actually uses to control the amount of ink being put on paper. CMYK devices can be linearised because one is actually controlling the amount of ink being used by the printer for each channel but sending RGB values to a printer which is using CMYK inks because there is no direct control over those various CMYK ink channels. But, one can certainly linearize a native RGB device such as a LightJet or other RGB laser imager because one would be directly controlling the amount of RGB which the imager will use when printing the photo. I’m referring the any style of RGB laser imager which uses RGB lasers to expose a piece of photographic paper which then needs to be chemically developed, same as if one had used a negative/slide to expose the paper through an enlarger.
In terms of averaging, the 3880 is so consistent there’s really not much or even zero need to average as it prints so consistently. To test this yourself, print a small target like the old TC283RGB from PMP or i1profiler. Print the target 2-3 times and compare them and then make up your own mind once you see the deltaE values for yourself. In the end, no matter what anyone tells you, it’s your time and effort and funds which goes into printing and subsequent measuring of all the targets you’d want to average. It’s really something much more useful for press use as they change with daily temps, humidity, etc. The 3880 or any brand profession level printer is consistent enough these days to make averaging not all that important or greatly beneficial.
Regarding number of patches, anything from about 1000-1500 or 1700 should be sufficient. There are minimal gains to be found if using 2500-3000+ patches. I find it best to print out a small target, such as the TC283 I mentioned and adjust driver settings such as ink density, perhaps increasing by 5% and another increased to 10% for example, and creating profiles from each and seeing if there is any benefit from the changes to density, or any setting one changes, perhaps using a different media setting, like Premium Glossy or Exhibition Fiber or Premium Luster or SemiGloss and seeing if that makes any improvement or beneficial gains.
What kind if papers do you mainly use? I use a few different baryta style papers, like Ilford Gold Fibre Silk, Harman Gloss Fb Al, et al. So I’ll change the media setting and once I’ve found the best media setting to use I’ll go ahead and increase the ink density and see if that helps.
Remember to always turn off your 3880 when not in use for more than 12-24hrs or so because the print head needs to be kept in the capping station so that clogging doesn’t occur. In the whole time I’ve had my 3880 I’ve never had a clog that needed anything other than the standard auto-head cleaning. I find it best to print a manual head test from the front panel LCD and if that shows up fine, all good. If any line or tiniest bit of something not printing correctly I’ll print another manual head test and in 95% of the time that’s all which I needed. I’ve only ever used genuine Epson inks and have a custom dust cover which I believe has helped in keeping nozzle clogging something which almost never happens to me.
Hope that helps a bit and if there’s anything you’re unsure of just ask away. We don’t bite here, I like to think that this forum is above that kind if silly and rude behaviour. We’re all just here to help. 
