Looked up how close could we get to the sun; The Space shuttle reinforced carbon-carbon heat shield is designed to withstand temperatures of up to 4,700°, if the shield wrapped the entire shuttle, it could fly within 1.3 million miles of the sun. Saturn is 886 million miles from the Sun. Surely getting 680 times closer would change this calculation; based on surface area enclosed at 1.3M miles and 886M miles, hydrogen concentration should be ~316 million x greater at 1.3M. Assuming it can be transported, instead of 3/4 million years, you'd be looking at less than a day, not 750,000 years.

Note even if we position the Ramjets 10M miles from the sun, the density should increase 700,000x and the collection time would be reduced to about 13 months.