You can optimize your PDF using Adobe Acrobat Pro and keep working as you do with Photoshop or whatever software you want. These software do not compress files the same way Acrobat do and do a poor job at it by leaving their own software data.
Yes, you can safely compress your files without losing any quality with Acrobat Pro. It doesn't only compress the images, it also compresses the structure of the PDF and cleans it.
A lot of businesses today use online printing services or upload their files to the system of their printer; file size cannot be what the designer wants and some efforts are required to optimize any PDF properly. On top of this, printing a heavy file takes longer time to process.
Adobe Acrobat Pro will crop your images that are out-of-frame to the perfect size, equalize your resolution to 300dpi+, remove private data and hyperlinks you might not need, flatten the layers, etc.
If you want to try this option, open your PDF in Acrobat Pro that comes with the Adobe Creative Cloud, and select "save as other..." in the menu file. Then select the "optimized PDF".
If you don't need to keep any elements such as layers or hyperlinks, you can safely check all the checkboxes you will see in the sections on the side panel (Discard objects, discard user dataa and clean up.) If you need to keep some features, simply look at what option does and don't check these boxes.
In the image section, you can add 300dpi to the field next to the downsampling feature. If you want to keep the maximum of your file size, you can still use 400dpi; it will not create any extra pixels if your images are lower than this resolution. It will lower all the graphics that are at higher resolution to this minimum instead.
You can do the same for grayscale (suggested 300-600dpi) and monochrome (suggested 600-1240dpi).
For each of them you can select the Zip compression. If you need more compression, you can use the "maximum JPG" compression if your layout contains mainly pictures.
If you use transparency, it's a good idea to put the transparency setting to "high resolution".
Then you can save this file using a new name just so you can see the result before overwriting your "full resolution" file. It should really help your lower the file size of your PDF.
PS: If you use text layers in Photoshop (which I guess you use), keep your resolution as high as possible.
These are screenshots of the 2 sections that will affect your graphics the most in Acrobat Pro.
As you see, it's all functions you already know about (resolution and transparency) and you really don't need to be a PDF expert for this! It's specially easy in your case since Photoshop handles transparency in a better way than Illustrator and InDesign. And if you end up converting your text to vectors as suggested below, you can still use Photoshop for your montage and background, and use your transparency there.
The other sections of Acrobat pro (while optmizing files) is more related to hyperlinks, bookmarks, private datas, etc.
Another trick that might work for you to bypass that Photoshop request...
You can save your Photoshop file as PSD with all the layers, and then open that PSD in Illustrator. You should be asked to choose between flattening the artwork or converting the layers to objects. This should keep your text layers in vector... and then you can vectorize that text (create outline), and export it in PDF again! You don't need to vectorize your text but it's better if you send this file as a print-ready.
It's also very safe to optimize as you can safely produce a "standard" .PDF and lower your image resolution to 300dpi without affecting the quality of your texts!
(See post about this here)