I would like to sell approximately $35000 in stocks currently held at Edward Jones. My total portfolio is approx. 1.5 million. Edward Jones will charge me 1% of the sale. Would it make sense to transfer those stocks to another company and then sell them at $10 per trade?
TLDR: Yes you can.
That is quite a steep price to pay for a trade. I've used TradeKing previously, which would charge you $5 for that same trade. Some other brokers are more or less expensive, and it is normally representative of the service one receives. One option would be Scottrade. While they are much more expensive than TradeKing, they offer a much higher level of service. Even at $17 a trade, you'll save a lot of money over the Edward Jones trade.
A big question here is who does your investing now? Most people are pretty horrible at managing their own investments. Some professional advice is probably in order. For most they discover this when their investments are small, mitigating any mistakes made. You don't have that luxury. I would highly recommend making sure you have people that can help you make good decisions.
The more I think about it the more I like the move to Scottrade (no affiliation) or one like that (Charles Schwab is another option). With Scottrade you can go into a local branch and talk things over. I think they offer some professional management as well. Schwab will offer the latter but not the former. However you can call them up and talk on the phone. Another option is to go with Fidelity and have them manage at least part of your money. Of course you can always just do a professional, independent money manager.
Another option is to renegotiate with Edward Jones. Something like: "Sorry but this is ridiculous, you need to do much better or I am moving all my money." Its much cheaper to charge you $100 for that same trade than lose the whole account.