I haven’t gotten around to testing the implementation in the TruncatedNormal R package referenced in Multivariate normal cdf. The neat thing is that it allows the non truncated and truncated versions.
I think it would be really interesting to see if it works with the algebra solver. You can try coding it in stan and we can help out if you run into any issues. If it works well then it’s a great candidate to be added to stanmath.