I have been trying to PCR amplify an ~3kb fragment from cDNA of THP1 macrophage to put restriction sites at both the ends so that I can use it for restriction cloning. My primers are 36bp long with 24 annealed bases, 6bp of the RD site, and 6bp for the enzyme to sit; they have a Tm of ~53°C with a GC content of 44.4% and 41.7%. I set up a gradient PCR from 47C-59C and didn't get a single band of good in any of the lanes (image attached). I eluted my specific 3kb band (gave an inferior yield of 4-8ng/ul) and used it as a template to put another PCR, expecting to see just one band (since, now, only my desired template should've been there taking isoforms also out) but still saw a similar pattern (as seen in the attached image) of smaller non-specific amplicons.
What can I do to have no non-specific amplicons either (so that I can proceed with PCR cleanup instead of gel elution to prevent yield loss) or increase the intensity of my specific band?