So, to pass on what I have worked out for getting mods to render on Dynmap.
Concerning the incomplete rendering when new chunks are generated...I have been using the forge version since at least 1.6 and never have been able to get that to work right. Occasional 'fullrender' or 'radiusrender' have always been needed to cleanly get freshly explored areas to update for me.
Concerning the modded blocks appearing black. The built in support for many popular mods appear to be broken as they are all still configured for 1.7 version of those mods. (can see this in the jar file) Back then, those mods had to use fixed block IDs which were set with config files. During launch Dynmap was written to look up those block IDs in the config files and attach the correct textures and models. Those textures and models were defined in the renderdata files internal to the Dynmap Jar and attached to whatever the current blockIDs were. Very smart system and worked great for 1.7.
Current versions (I think since 1.8 or 1.9) of mods do not have to use a defined block IDs and instead use a modname:blockname format. When minecraft builds a world the block is given BOTH a numerical BlockID and the modname:blockname identifier.
The mod support within dynmap STILL EXISTS, it just requires that you set up your own custom models.txt and texture.txt files within the /dynmap/renderdata folder. (See the WIKI)
From within a loaded world in your modded game you should be able to look up the current block ID of the modded block you wish to render. Use that block ID to build a custom models.txt and/or texture.txt file to allow Dynmap to have the information it needs to render the data. THESE IDs WILL BE DIFFERENT FOR EVERY SUBTLE DIFFERENCE IN A MODPACK.
I built a few example files for Biomes-O-Plenty that can be updated 'reasonably' easily. The idea is that only the variables defined in the header needs to be updated with the correct block ID numbers found in JEI (or simmilar).
If Dynmap is able to read the modname:blockname format I have been able to determine the syntax needed and would love see someone figure it out....but in the meantime, this works.