BJJ cross training at Judo academy?

Any one start in BJJ for a significant amount of time and then start cross training at a traditional Judo academy?

I’ve been training BJJ for 16 years now (I’m a Ronin Brown belt; never bothered to get a belt flair), and I want to get competent at throws in the gi. I have a bit of wrestling so I’m not clueless on the feet, but I wanna learn foot sweeps and throws and apply them effectively in a BJJ context.

I’ve got two concerns:

1. Some judo techniques leave your back exposed. There’s all sorts of Judo tendencies that go against BJJ principles…

2. There’s such a difference in how Judo academies train vs BJJ. Im not sure how much of the Judo curriculum can apply to a BJJ context.

I know guys like Danaher, Glick, and Shintaro have spoken on this topic a little bit, but I wanna hear from those of you who’ve managed to successfully crossover from BJJ to Judo and apply it in BJJ. Can this be done training in a judo academy? Or should I be training my sweeps and throws in the BJJ gym?