The downside of trying to make a logographic conlang is it's not in Unicode and never will be. If they didn't let Tengwar in they certainly won't let my stuff in, and a logography is a much bigger ask than an alphabet anyway.
@icefox @Azure There's ConScript http://www.evertype.com/standards/csur/, and then Under-ConScript http://www.kreativekorp.com/ucsur/ since ConScript seems to not be updated, though both of them are broken over HTTPS and that's not very confidence-inspiring.
Still, if you want to use the private-use codepoints that might be a good place to check first.