What I’m hearing nowadays is that you can block the legs if you anchor a legal grip above the belt. I would risk it because it’s only a shido if it goes wrong and I’m not an international badass who needs to worry about this shit
I love judo but I mainly train BJJ. I use judo for my takedowns rather than wrestling due to knee pain. But if some did this to me, rear naked or back take is easy
There are some grassroots organizations in the US like Freestyle Judo that allow leg grabs and more newaza. Also, the USJA is implementing a "Kosen" division in some of their tournaments, which has less restrictions and a deeper focus on newaza.
Combining the cross grip and the "illegal" variation appears like it might mitigate the risk of having your back taken. Definitely want to test this out in class to see if it's as applicable to BJJ in reality as it seems to be in my head.
It's definitely more effective with the leg grab, but as someone who has practiced both judo and BJJ for many years you're better off learning other techniques for BJJ. A standard kouchi gari into kibisu gaeshi (ankle pick) is less risky in terms of back exposure.