Usually closing costs are between 2-3% of actual sales price for a buyer.
I would think that one lender should be able to produce both types of loans. So, you should find a lender that will pick up the Closing costs, and find you a grant.
If you'd like you can contact me directly and I will forward you to an LO that is familiar with both plans.
Yes, it is true, that you don't want too many people pulling your credit, however, if they are all LO's and within 30 days. It will count as one pull. Especially when purchasing a home.