We use sendgrid and are pretty happy with deliverability rates (we have our own dedicated IP with them). I know postmark and amazon SES offer similar features but never used them.
Have a comparison between the twitter predictions and the bookmakers odds. Have a 'Place Bet On This Match' link with referral link embedded on each one.
See if there's any affiliate programs you can join as well where there's a "Free £10 bet on any world cup match" and you get a %.
Yes i've tried Freshbooks and was impressed with the overall experience, but it seems more geared up towards time and materials based charging and invoicing, rather than expenses and general business accounting.
Get somebody to take a look at your service/idea who has some experience in the B2B market. Talk about it.
Maybe you're so in to it, you don't see what's missing.
I think it's especially hard because you're on your own. Try talking about it with friends or family. They'll mostly give some high level advice, but you'll see it will give you comfort to a certain degree.