You need to have long primer annealing and primer extension steps. Try with 1 min primer annealing at 60oC and 4 min extension at 72oC. yes it is a long PCR but possibly it will work. If you have an access to a gradient machine, you can test several annealing temperatures at the same time.

Thanks for your answer.

I tried 30s annealing and 2min40 elongation at 68°C (I followed the Expand HF protocol actually). But I can try with a gradient machine and your recommended T°C. Should I try adding DMSO ?

If you are having some inspecificities DMSO could make an improve, but it makes thinks a little bit harder too. Adding some extra magnesium helped us in our Long PCR project. We also tested different Tm (with gradient machine) and long extension  (around 5 minutes!). For teh anealing, with 30 sec is enought.

The amount of DNA was also critical in our project. Adding 50ng (total) of gDNAs wasn't enough, it worked much more better with 100ng of gDNA.

Hope it helps.

Thank you very much.

DMSO worked without changing the PCR program. I got the 4-kb band!