When your SD is inserted, you can't boot from eMMC. The rest looks ok ... if you did an update and upgrade, you don't need to download any 3rd party boot loader. I don't know if it's ok but let's assume it is.
The reason is simple. If you insert a card when the board boots the H3 will always search for a bootloader there. If you insert the card later it won't be recognized (which might be able to be fixed by playing around with /proc/driver/sunxi-mmc.x/insert).
So to boot with inserted SD card the bootloader has to remain there and point to the rootfs on the eMMC (the numbering of devices will then also change!). This can be done by using our nand-sata-install.sh script and then not wiping out the SD card but keep the 1st MB intact and only adjust the partition table so that the SD card can be used for data.
Addendum: Here you find instructions how to get the kernel to recognize an SD card that has been later inserted and that is correctly defined in script.bin as 'manual': http://lists.phcomp.co.uk/pipermail/arm-netbook/2013-October/009162.html