How can I change not only the value of the custom field but the what the field shows itself?
I'm by no means a PowerBI expert, so there may be options I'm not aware of. I don't think that there is a tidy solution to this in PowerBI, as this is not quite what BI tools are usually intended to do. However, it can be done-- you'll just have to accept a degree of hack/kludge character to your projects.

The most straightforward approach I can think of is to make a new table for your presentation values, with something like a column for each company and then another column for "meaningful data to present". That latter column should be set to something like text, so that it will display different values with the correct conventions (dollar signs, comma placement, etc.). Then, when drawing on data to populate the report, set the card (or whatever structure you're using) to draw from that presentation table. Since field1 will always contain the correct data to display for a given company, and that field is formatted as text, you won't have to worry about mismatched data types.

This approach will require some preprocessing of your data, so that the presentation table is populated correctly for each distinct company whose data you are presenting, but it's nothing that a SQL query can't produce pretty easily. This can be done within PowerBI or externally, with the presentation table imported. Importantly, you will not have the option of using aggregations or similar operations (that would be the case anyways, with this type of report output, but it's worth mentioning explicitly). This will be, essentially, a display-only report.

The key is that field1 (using the naming convention in the question) is representing something unstable in the data itself (different data types in the same field), but relevant in an "above the data" sense.

As a final note, I'll encourage you to consider whether or not this data really belongs in a single, conglomerated report. That might legitimately be the case, or it may be that this structure is demanded by a superior (whether it makes sense or not). But maintaining a single, kludge-filled report like this might ultimately be more work (and less valuable) than multiple reports which fit better with PowerBI's design favoring strongly-typed data fields.