Must one re-perform the prayers that were offered after an insufficient ghusl, given the uncertainty of their number?

Immersing the entire body in water for prayer without observing the order of ablution (Wudu') parts is not sufficient according to the majority of scholars. However, it is sufficient according to those who do not consider the order obligatory, such as the Hanafis and the Malikis.

If you washed your entire body with the intention of removing minor impurity or making prayer permissible, your impurity has been removed according to the schools of thought that do not stipulate sequential order. This opinion is disfavored, but a fatwa is issued based on it to ease matters after the act has occurred and to avoid the hardship of rectifying it.

Therefore, you are not required to repeat past prayers, but you must observe the sequential order in your ablution in the future.