I signed up just to say thank you for all the information in this thread. Thanks to all of you I don't have to redo the REALLY boring beginning of MH4U OR carry my retail cartridge around.
Just to attempt to summarize to try and save someone similar to me some time (Sky3ds, Retail cartridge, access to an old 3ds, no gateway card, New3DS with latest firmware) This will assume you have done some research but should take some trial and error out of it. This will let you play your rom online and use your save from your retail cart.
1. Dump your retail cart
Download the latest gateway firmware, add Launcher.dat to your SD card (in the normal SD card slot, big enough to hold your game) and the contents of the blue card folder to your sky3ds sd card (formatted with a normal PC) and insert it into your old 3ds (firmware <9.2). Open your 3ds browser, and clear your cookies from the settings menu, then browse to go.gateway-3ds.com. Your 3ds screen will flash white, when it does hold down the L button to launch the gateway menu. From here, change to your retail game cart then choose backup game cartridge, then backup save.
2. Make your template
download the Gateway rom patcher (I used v1.1) open it, then open your dumped rom (from your normal SD card) to get your card ID and chip ID. Download SkyTempIdEdit and the latest sky3ds template and put them in the same folder. press windows+r to bring up the run box, type the following and replace each <> with your info: <path>SkyTempIdEdit.exe <CardId> <ChipId> You can also check the instructions that come with the tool for reference. Rename the new template to something you will remember.
3. Flash your personal rom
Open the sky3ds disk writer and format your microSD for your sky3ds. change template to your newly created one. Then drag your dumped rom to the card.
4. Convert and load your save
rename the .SAV file you dumped earlier to anything else. Download and install ActivePerl on your machine. Download duke_srg's awesome Perl script and delete the .txt extension to leave you with a .pl Open a command prompt and browse to the folder where you have been putting all this 3ds crap (templates, roms, etc. you put it all in the same folder right?) type: perl skysave.pl <template file name.txt> <save file.SAV> <cart code (4 letter code. Monster hunter is BFGE)> This will create a .SAV named with the 4 letter game code
If you have been using your sky3ds, make sure your private rom was NOT the last selected game.
In sky3ds disk writer, right click your private rom name and choose load save file. Point it at the new .SAV
Load up your game in sky3ds, enjoy your backed up save from your retail cart AND online play since you are on a personal header.