Q: Can't boot into Bootcamp/deleted EFI file

I deleted my EFI files/partition and couldn't start in Bootcamp. I was able to make a new EFI partition, but I still can't start in Bootcamp. I see it as a startup disk in System Preferences, it shows up as a device in Finder, but I don't see it when I use the OPTION key to start my computer.

When I run diskutil list, this is what I get:

/dev/disk0 (internal, physical):

   #:                       TYPE NAME                    SIZE       IDENTIFIER

   0:      GUID_partition_scheme                        *750.2 GB   disk0

   1:                        EFI EFI                     209.7 MB   disk0s1

   2:                  Apple_HFS Macintosh HD            449.3 GB   disk0s2

   3:                 Apple_Boot Recovery HD             650.0 MB   disk0s3

   4:       Microsoft Basic Data BOOTCAMP                300.0 GB   disk0s4

When I run sudo gpt -vv -r show /dev/disk0, I get:

gpt show: /dev/disk0: mediasize=750156374016; sectorsize=512; blocks=1465149168

gpt show: /dev/disk0: PMBR at sector 0

gpt show: /dev/disk0: Pri GPT at sector 1

gpt show: /dev/disk0: Sec GPT at sector 1465149167

       start        size  index  contents

           0           1         PMBR

           1           1         Pri GPT header

           2          32         Pri GPT table

          34           6        

          40      409600      1  GPT part - C12A7328-F81F-11D2-BA4B-00A0C93EC93B

      409640   877533368      2  GPT part - 48465300-0000-11AA-AA11-00306543ECAC

   877943008     1269536      3  GPT part - 426F6F74-0000-11AA-AA11-00306543ECAC

   879212544   585934848      4  GPT part - EBD0A0A2-B9E5-4433-87C0-68B6B72699C7

  1465147392        1743        

  1465149135          32         Sec GPT table

  1465149167           1         Sec GPT header

When I run sudo fdisk /dev/disk0, I get this:

Disk: /dev/disk0    geometry: 91201/255/63 [1465149168 sectors]

Signature: 0xAA55

         Starting       Ending

#: id  cyl  hd sec -  cyl  hd sec [     start -       size]

------------------------------------------------------------------------

1: EE 1023 254  63 - 1023 254  63 [         1 - 1465149167] <Unknown ID>

2: 00    0   0   0 -    0   0   0 [         0 -          0] unused     

3: 00    0   0   0 -    0   0   0 [         0 -          0] unused     

4: 00    0   0   0 -    0   0   0 [         0 -          0] unused

Is there any way I can fix this, or do I have to destroy my Bootcamp partition and start from scratch?