As far as i know, nope, there's no safe container apart from the one at the very begging of the DLc where you join the happy Trail caravans. Homever, you can go back to the Mojave anytime you want to store your items.
I used the workbench foot locker thing in Angel Cave for all of HH without losing anything. I did take everything with me when I returned to the Mojave though, so I don't know if your stuff will disappear when you leave.
Unlike TES most containers in FO3 and FO:NV are not set to re-spawn.. But it will always be trial and error.. I have used both Angel cave, and park ranger outposts without any hassle...
I used the workbench foot locker thing in Angel Cave for all of HH without losing anything. I did take everything with me when I returned to the Mojave though, so I don't know if your stuff will disappear when you leave.
i always use the containers in angel cave too, and like you, always take everything when i'm done. never lost anything in many playthroughs.