Hesitation Motor under light load up gental grade & oil use

I have a 2000 Lincoln Town 4.6L car with 134,000 miles. Question when driving abound 35 to 40 MPH up the slights grade and lightly apply pressure to the accelerator to maintain my speed I have short hesitation. If I give it more it stops. Jumping onto the Interstate and floor it no problem. About this same time this started I also started to use motor oil. About a quart in 1500 miles. No smoking out tail pipe or leaks. I know limo service people who have put easy 500,000 on their Town Cars and none have had this problem.
Any help will be appreciated as I love this car and it my 4th Lincoln the last one was 17 years old and a few miles short of 200,000 and no problems except the AC compressor went out.
Fred