Personally, I have only tried one conscript, which I began working on earlier last year but suspended to work on my discovery of the Gujarati origins of several scripts in Indonesia and the Philippines.
It's a script for writing sign languages and can be adapted to any and all. I started on it because, as a sign language linguist, I'm aware of the difficulties with the current set of notation systems for sign languages. Stokoe notations and Hamburg Notation System (HamNoSys/HNS) are too linear in structure and overly complex in certain ways. Older systems (Bébian's 19C Mimographie, LaMont West's system and other alphabet-based systems) are even more ill-suited, and dance notation-based systems like Benesh, Labanotation and Sutton SignWriting(TM) (SSW) are at once poorly suited to a linguistically-oriented transcription and too complex for computer use compared with ordinary plain text-based systems.
Still, dance-type notations have the advantage that unlike text-based systems used up to now, they are two-dimensional — a fact that lets you map a lot of the complexity of sign structure (from phonology through morphology right up to discourse) onto the structure of the notation itself. You can't do this with anything close to the same simplicity with any of the one-dimensional, purely linear systems like the Stokoe-based systems or HNS.
Realising that a Tibetan- or Han'gul-like structure gives you that extra second dimension to work with, I started putting together a script that takes the way dance-based notation (SSW in particular) use both dimensions of space on a 2-D surface, and brings it together with the discrete, finite way characters are combined in the uni-linear alphabetic systems. (SSW arranges its characters in 2-D space by x,y coordinates. In this way it is much more of a "Lego block"-type system for "drawing" certain aspects of signs with, rather than really "writing" them in the way "writing" is normally understood. This is one of the things that makes it so difficult to use on a computer and requires special, complex interpreting software. You can't just "type" SignWriting in any computing environment the way you can with other scripts: it requires special composing software and then obliges you to paste images of the result into another environment.)
The system I came up with owes a lot to Han'gul and Tibetan for its structure. Because its base characters are made up of Chinese-Japanese-Korean-type strokes and with similar stroke orders, and the rules for combining characters in blocks result in an overall look that is reminiscent at once of Han'gul, Chinese characters and Japanese kana, I call the script "Sign Language Moji", Moji being the Japanese word for a character or letter. Handshapes are extremely iconic and easy to remember and write and the set of body part and space markers, as well as direction markers, are designed to be maximally iconic or mnemonic.
The script is designed to be typed quickly and easily (though underlyingly it is similar to Indic scripts in its typographic structure and needs a similar type of layout engine), and to easily represent 3-D aspects of sign language structure that don't exist in spoken languages: use of space, detailed locations for broad location areas on the body, hand or in space, simultaneous use of distinct signs or sign parts on each hand, eye gaze and other nonmanual markers, and the all-important use of body- and eye gaze-shift in discourse to represent constructed action and constructed speech. For this, I use a system of angled arrows based on "guillemet" quotes («») that both enclose the relevant text to signal a quote and point in one of eight directions to indicate the orientation of the signer's eyes/head/body.
Because of the way it is designed, the system is likely to be the most useful one yet available for simple writing or transcription of signs, once I am able to design the actual font(s). It's doable by hand at the moment, but unfortunately, that's not enough in our computer-based world, and especially when nearly all useful sign language transcription and research needs to be done on computer to take advantage of corpus-based research tools. Still, the system is ready to be used for most sign languages (the only main disadvantage being that it doesn't have handshape symbols yet for all known sign languages, but that is easily remedied with the consistent, rule-based and iconic way handshape symbols are constructed.