Looking at the specs of the Akai EIE Pro (from here), this is the relevant section:
Mic gain (MIC): +9dB to + 51.5dB
The mic preamp in the Akai is capable of putting out up to 51.5 dB of gain.
Looking at the spec sheet for the SM7B, search for "Output Level." You'll see that the output level for the SM7B is -59.0 dB. This means that even at max volume (not recommended) loudest the Akai can get the SM7B is -7.5 dB. You start hitting the top 20% (the hissy section) of your preamp gain at ~40 dB. This gives you up to -19 dB with clean gain.
Simply put: Your preamp isn't capable of putting out enough gain to support the SM7B. You need between -18 and -12 dB of clean signal to get a good tracked recording.
The options you mentioned such as external preamps and new interfaces are both valid options, and probably the best plan in the long term. However, preamps and interfaces can get expensive, so I'll suggest a third option.
You said you tried boosting the quiet signal by adding a gain or compression plugin, then increasing the output gain of the plugin while setting the plugin to make no changes to the relative content of the signal. This will increase the overall volume of the recording, which increases the noise floor as well. You may need to gate the signal before gaining to limit the amount of the noise floor which makes it into the final recording. You can also attempt to lower your noise floor, but this is very difficult to make a significant difference without a significant investment into acoustical isolation.
The other option is an external gain booster, such as the Triton Fethead. This is a very simple inline preamp that gives a flat 20 dB boost to your line volume before it hits the preamp. This would give you plenty of headroom to make use of your SM7B, and would be simple enough to use on other mics as well if needed.
You might check out this thread discussing the amount of gain needed for the SM7.