Every time someone wants to print a file at 300 PPI on sizes beyond 1 m, I really wonder if they needed it. Well, in reality, I know they do not.
Let me explain some things about the 300 PPI "myth".
Let me start with a flat sheeted offset, for example, a movie poster of good quality of course. On the prepress process, these images need to be transformed from pixels to lines, at the end we will have a print of about 150 LPI. This is the normal lineature you see in a fashion magazine, depending on the print quality this can be great and detailed images. A magazine is intended to be viewed at 30 cm.
From a mathematical point of view, we do not even need 300PPI, but the Lineature multiplied by the square root of two. For 150 LPI this will be 150 x 1.414 = 212 PPI.
Of course, the maximum size of a flat sheeted offset machine is around 1 m, let's say 1.2ish on really big machines.
The size you need is obviously a digital print.
On a digital print, this transformation does not take place (only in really rare cases) this means that you will have more final resolution with a 200PPI file than a 150LPI print.
You can even use 150 PPI and you can barely see an isolated pixel at 30-50cm.
A really expensive camera of $50,000 can have a photo of 100Mpx. This kind of cameras are to make big prints from people with egocentric issues :o) let's say a Hollywood actor that wants a self-portrait of about an entire wall.
Remember the numbers: 100Mpx... you want a file of 36,023 x 31,889 which is about 1,149 Megapixels.
It is ok if it is an awesome panorama of the city and you want to see the faces of the townsfolk. But really, 150 PPI will be 1/4 the image and still will be an excellent print.
A Magazine (let's say 30cm height) is meant to be viewed at 30cm. A wall-sized image does not. It is meant to be viewed at, let's say 3 m. This means that the same image that you use on a 30cm magazine can be used on a wall.
A printer provider will probably transform your image. No one wants to process a file of unnecessary size.
One more thing I need to say is that probably you did your project in the wrong program.
As already commented, an EPS file is asked when you have vector elements, so Ps is not the right tool.
One last thing. Do not trust me. Make some test files with the same provider. On the small size of A4-Letter size print. Make one file at 300PPI, one at 250, 200, 150, 100PPI and make a decision.