AXD's got various features which require mode setting (e.g. for selecting between multi-device synchronization mechanisms that it supports). This would need an enum control, but I guess that this could be fudged with mutually exclusive switch controls for each of the enum values. AXD's also got numeric configuration parameters which it needs to be able to receive (e.g. parameters for stream synchronization heuristics, audio filter coefficients, etc.). Maybe a volume control with a domain wide enough could be used for this kind of configuration parameter. It's rather horrible, but might be fine for while the AXD driver is out of tree and there aren't more appropriate ALSA control types (e.g. enum and non-volume integer). :-/
I am not too sure I understand what you refer to as synchronization or multi-device synchronization mechanisms. Since you mentioned you only need an initial time, I wonder if this is conceptually related to the start_at() functionality discussed last year for PCM?
If you have a set of implementation-defined mechanisms related to algorithms, why not use an ALSA binary control where you define you own syntax and content and use the alsa control layer as a 'dumb' pipe between user and kernel. That's what everyone does for DSP control.