Does CAO100.7 apply to private ops?
Yes, see CAO 100.7.1 in this link
https://www.legislation.gov.au/Details/F2018C00475. Also CAO 20.16.1 comes into the act. See CAO 20.16.1.1 in this link
https://www.legislation.gov.au/Details/F2018C00462 and CAO 20.16.1.3 in the same link. Likewise have a look at CAO 20.16.2 and 3.
Is it really this complicated to use a EFB to do a W&B for C172?
Not at all. However, a problem may arise with establishing whether the program proposed for use is valid .. or not. Refer to CAO 100.7.5.2.(2) in the link to see whence the procedural problem arises.
Unless you wish to expose yourself to censure, one needs to address these considerations. Providing you observe the loading system, you are reasonably well covered. I don't see a problem with developing a WCO workaround with a simple loading system which permits the use of an EFB to do the number crunching. Just make sure that the EFB is legit from a technical viewpoint.