Restore Wii without SD card. I have NAND Backup.

Afaik, the only other way is a hardmod.

Tried reformatting the card?

 

Any reason why you want them reinstalled?

 

I would first run syscheck to see if the required ios are already installed.

Touching ios 80 could be dangerous without bootmii as boot2, although I believe it is possible to install stock ios I don’t know the best current tool.

That said, according to the page:
NOTE if step 6 fails: BBL installer grabs the required IOS modules from your Wii's NAND. If your Wii is not updated, it might be possible that the installer won't be able to find some of the required modules. In this case the installer will try to get those modules from the following IOS wads that must be placed on the root of your USB drive:

• IOS36-64-v3608.wad
• IOS58-64-v6176.wad
• IOS80-64-v6944.wad

 

Run your syscheck, then open it using modmii.exe, and it will tell you how to go about making all the necessary improvements. It will generate a custom guide based on your syscheck, follow this guide with some modifications. First, save everything to your fat32 HDD instead of sd, and the second thing is probably implied, but access your homebrew channel via priiloader

Edit: have no fear, u should be able to easily recover, u just can't use bootmii (or neek) until u repair your sd card reader

 

I literally spent 5-10 min trying to scroll down your syscheck on a mobile device, it's freaking impossible, I gave up. Just paste your syscheck here in a spoiler like a normal person, lol

Or open your syscheck using ModMii as I advised previously

To fix your upside down homebrew channel u can use modmii's hackmii solutions guide, but it's not necessary if u are using modmii's syscheck updater wizard... Although if your hbc is still upside down after using the latter, then try reinstalling the hbc even though you're on the latest version already. I don't think this will be necessary though

Edit:

I finally managed to see the rest of the syscheck log, it's as I suspected, somehow u have a custom IOS58 installed as version 65535. Since the homebrew channel is installed to run using this slot, it is upside down to troll u for tinkering with this ios. Installing a clean IOS58 should be enough to remedy the upside down issue, if not, install a clean IOS58 then reinstall the hbc as well

There are some other interesting things about your syscheck. Like u have random cios installed to slot 240 and 241 and 251 which are uncommon slots to use for anything

U have an older version of cios249, but your 250 is very current (v10 beta 52 is the same as v8-final, and the latest recommended cios). Generally d2x v8 final cios with base 57 is recommended for slot 249 and base 56 for slot 250, but it really doesn't matter if u get it reversed.

Your system menu IOS, IOS80, has had its version number maxed out but no patches applied

U have a patched ios31, which is generally not recommended, but it may be necessary for riivolution. I know they patch ios31 but I'm not sure if/how their patches appear in a Syscheck log.... but doubtful that it's from riivolution, because that would have had u install a patched system menu IOS80 in addition to 31, so really no idea why ios31 is patched. It's not uncommon to see ios36 patched, but ios31 is truly unique and I don't know why that is the case for your wii

U have stubs installed to slots 222 and 223,while it doesn't really matter because u only need one or two good cios's, these 2 slots were used for hermes cios's

ModMii will recommend solutions to all I listed above and more (like extra brick protection in the form of patched system menu ios's on slots for different system menu versions to protect again accidental/improper downgrades/upgrades/region-changes)

 

It should be more than 6, probably ios 31, 58, 80, 202, 222, 223, 249 and 250

Plus all the extra brick protection system menu ios's, so 70, 60, 52, 50, etc.

 

Ah yes, u used the hackmii solutions guide, that explains why just 6 IOSs were downloaded. Improvements to your setup can still be made by using modmii's syscheck updater wizard/guide. But I guess if u are happy, then mission already accomplished