The way I look at this with this additional information is that the papers are with H's lawyer and there's been no movement from their side despite your lawyer's efforts to get some type of response from the attorney.
With this complex business transaction, I think it would be best to stick with your lawyer to assist you in navigating and negotiating through this process. Making statements that you are "able to do it without lawyers" just makes it hard for you to back out. In the future, it would be advisable not to make these type of statements that will allow H to come back and accuse you of 'dishonesty.' Please keep this in mind, ok?
If I were in your shoes, I'd do the following in this order:
1) Wait for H's response to your recent text 2) Depending on the content of H's text, I would put forward to him: "The papers have been filed with your attorney. Please check with him/her since we have yet to hear back from him/her." Keep it simple and be sure that the onus is on H to get this moving along. 3) Regardless if he elects the court route or the mediation route, you'd still retain your lawyer to protect your interests
Ellie and Job may be able to offer some other suggestions and options.
