Build Your Workflow in Advance
Use the tools you know and love, but make a plan in advance for how you will collect and organize your research log, your notetaking, your images, and your citation documentation.
Prioritize and Strategize
Use your finding aids to prioritize which boxes and folders are most important to see first; then list which ones you will see if you have time. You can then set up a storage and naming system that will make it easier to store the images that you take as you go along.
A mistake that some researchers make is to think that because they have a camera, they can just photograph everything and look at it later. You need to know before you go how large the collection is and how manageable it will be to get through.
Create a Personal Policy
Sometimes you are better off not taking a photo:
Photographing documents may mean you can shorten your research trip and the associated costs of travel and hotel, but it does not save time in the long run.
Remember that scanning/photographing a document is only putting off the real work of research:note taking and writing. While a computer full of scans might be handy to refer back to if you ever need to verify a quotation, the process of organizing, storing, and retrieving documents you collect while researching can become a full-time job on its own and can act as a form of productive procrastination. Eventually, you will have to read and take notes on the archival materials that you collect. It's best to make good decisions on when to slow down and take notes during your research rather than just accumulating a large number of documents that you will have to sort through later.
You might want to create a policy for yourself on when to photograph and when to take careful notes. For example: If you find you are transcribing more than one paragraph, consider photographing it; otherwise, prioritize boxes and folders that are most important to you and move more slowly through documents.
Allow for serendipity: other benefits of slowing down are that sometimes as you work, the documents will lead you to other places in the collection that you hadn't planned.
Zotero in the Archives
This guide is very helpful for using Zotero in the archives. It does not, however, cover using scanner apps rather than using the camera as your main tool for retrieving images. It also recommends using Dropbox and linking files in Zotero. I think that is one solution, but consider getting a subscription to Zotero anyway. It is not too expensive and will free you up to use Zotero from any computer.
Organizing with Phone and linking to Dropbox
Predetermine your naming and organizing schemes.
Before you even take your pictures, decide how you are going to organize your photos and how you are going to rename the files, if at all. If you plan on keeping them organized in folders that mimic the organization of the collection, use the finding aid to determine which boxes and folders you want to look at and go ahead and set them up so that you can automatically save them to the right folder.
Keep a Research Log
Keep records of what files you plan to look at and what you have seen. You could do this in Zotero, for example, in the record that links the finding aid, or in a separate document.
One example is to set up all of the folders/ boxes/ and collections you plan on seeing by creating files in Dropbox or Box using a nested naming system. Both of these apps allow you to use a Comments feature. Even if you find nothing in a box that is worth photographing, you should note what you have seen.