Ok, so the rant is about the HR department and technically not the immigration department.
There is some amount of flexibility in Hong Kong.. which tends to be far more efficient than *any* other country I can think of, specially EU / North American immigration departments.
The receipt of the visa application should have a case number and a fax / phone number.
I would recommend two things 1) email the immigration department at
enquiry@immd.gov.hk and plead your case out with them.. they listen and 2) make sure you fax the immigration department on the fax number associated with your case.
If possible get the HR department to issue a letter pleading your case, saying you're required to be in HK on ASAP due to business reasons -- typically something like a client contract or a time sensitive issue. We know several companies that are able to plead their case effectivly and get visas issued within days.
I would also recommend escalating the hardship issues to your HR department and the senior most person in your husband's business / department -- to make sure they know you're going to suffer a fair bit of hardship due to the delays which is their fault and request that they figure out a way to compensate you.
P.S: Again, if you think 4-6 weeks is long .. consider how tedious an H1 application in the US is ... and possibly a similar work visa application to your country.