if your primers exactly flank that sequence then your product is very small so will not trap much ethidium bromide. It will also diffuse into the gel by thermal diffusion so may look weak even if there is a lot of it but can you give details of primers and amplimer size please. How are you measuring the yield of product. If you are using UV/nanodrop are you purifying the product before measuring the amount amplified?
You can design restriction sites and clone the sequence into the plasmid. Then use the polymerase and try to see whether it can amplify or not.Design primer plasmid and insert specific.
I may be misunderstanding your technique but it seems like a single extension of a 500pM of template. In this case you cannot get more than 500pM of double stranded product so ignore my first answer which assumed a pcr reaction.There is no amplification just a double stranding of all of your template so how to best optimise product . You should not have equimolar amounts of primer and ntps because this is a practical not a theoretical reaction. To maximise product you need an excess of reagents so that all of the primer anneals and to make it easy for the enzyme to extend there should also be a large excess of ntps . you probably need to run an experiment with different large excesses of primer and ntp but in PCR you have thousands of millions of fold excess of reagents but in your case perhaps only 100x excess-1000 x excess might work so just make sure you havea large excess, If you think that hairpin is a problem thenn try the reaction in 1M betaine or 5%DMSO either of which will inhibit hairpin looping, I am most concerned with the small amounts involved . This is a small amount (500pM) of extended product so is your visualisation method ( silver stain,dye) capable of seeing the amount that you load of this small length product?. I am not familiar with HPLC lower detection limits but check carefully with whoever is running your samples that the amount loaded is within the detection range for the instrument you are using. You might also try extending at higher temperatures...the vent is fine at high temperature so if the primer can anneal then a higher temperature will make hairpin less likely as the repeat is a poor candidate for hairpin with 1 in 3 bases mismatched