I've been discussing this with XDA member gilrad and below is his solution. If this can be refined to figure out issues with battery usage, etc., I'd like to include this in the general information post.
Northeye's blog also seems promising (Northeye is the developer of the MSS Req apk mentioned below). I also recently found mod.Email for Froyo, which is based off the default mail client, supposedly supports emoji, and seems to support softbank mail according to some commenters.
In the market, I searched for Softbank, two of the higher apps on the list is Softbankメール, I think that's the official android app from Softbank. Lower on the list is Softbank MMSReq, by Northeye. After adding in the Softbank MMS APN info (google search can get you that, there's a thread at Modaco iirc that gives it all), I run MMSReq, and manually request messages. After it does its magic I am able to download MMS's from the Softbankメール app. Since Softbank's servers handle the MMS->email conversion, there's really not a whole lot of configuring needed outside of adding the proper APN info.
Though as I mentioned before I have this suspicion that either the Softbank app or the request app eats away at battery life, so I disabled all automatic updating and basically manually check my mail once a week or so while relying on gmail for everything else. It looks like the request app can automatically download messages, though I never tried it.
From what I understand the way Softbank's email system works, 1) emails are sent to the Softbank-side servers, 2) they're converted into short text messages, then 3) they're sent to your phone number as an MMS notification at first, the process of which is automatically routed by their servers. 4) From there the notification is flagged for download (most phones automatically download them without telling you about the notification, but Android phones give you the option to manually choose and download them), at which point the Softbank servers check your phone's UserAgent, and 4) if it matches a whitelist then they will send you the full text.
For the Softbank mail application, its pretty much a modified version of the default Google MMS app. Pretty much by the time you receive the email, it's treated entirely like an MMS, so I would say its apt that the app used is an MMS app. In fact, you can actually receive MMS notifications under the default Google MMS app, but downloading them results in failures, likely because they see a nonstandard useragent. There's also some modified MMS apps available from Modaco which spoof the UserAgent, but I couldn't get them to work on my hardware, Dell Streak (one force closes, the other fails to download).
If I were to guess (though I haven't even read the description of the MMSReq app as its all in Japanese and I already got it to work so I don't really care), the MMSReq app probably checks any non-downloaded MMS notifications, then sends a download request with one of the whitelisted UserAgents. Its possible this could work with other MMS apps, but as of now the only combination I found that works with my hardware is this and the Softbankメール app.