Looking at your file geodatabase and feature classes and at the axf file, I am a bit confused by your approach here.
With regard to the file geodatabase, there are a couple of problems. Typically, one would name feature classes something sensible that describes the contents of the feature class. Naming a feature class "Point", "Line", Or "Polygon" doesn't seem sensible nor descriptive. A number of domains have been created to represent aspects of what seems to be a single numeric priority ranking from 1 to 3, yet there are 6 domains where it would seem there need be only one with coded domain values 1 through 3.
With regard to the axf file, each feature class has it own custom edit form and identify form defined yet each feature class only contains 4 or 5 fields. This would not seem to occasion setting up custom forms as there are not enough fields or data to be collected such that it needs to be organized in pages.
I might look at those issues first before proceeding further.
Assuming those issues have been assessed, I question as to why one would need to or want to set up a custom workflow in custom forms in this situation. ArcPad already provides the functionality that is required.
First, by creating a layer definition for each Problem Type subtype that has been created, a list of each Problem Type subtype and its associated geometry will be created in the Start/Stop Editing Tool. While a list of 30 feature types may not be ideal, at some point a layer will have to be closed for editing, so unless one intends to create yet another custom form to end editing or script an end to editing, the user is likely to have to use the Start/Stop Editing Tool anyway, so he or she might as well start using it from the first.
Second, selecting whether a feature is captured by pen inputs or GPS is already handled by menu items in the Edit toolbar; however, the process for each input method and each geometry type is so different that no single button to select an input type will handle the task. Creating a single point is a lot different from creating individual vertices or continuously adding vertices for polyline and polygon features from pen and GPS sources. Users will have to know how to complete these very different tasks and it will only benefit them in terms of their professional development to learn how to create and edit features in ArcPad in the default manner and not in some scripted and idiosyncratic workflow.
So my suggestion would be to use the existing capabilities of ArcPad instead of attempting to create a custom interface/workflow for your users, because users will likely have to work with the interface as it exists for most task and it is to their professional benefit to know how ArcPad actually works.