To be blunt: Garbage in = garbage out. Per dave_in_nova's comments - you can shear this one till the cows come home, and it is still going to be a piece of cr@p. It even appears that you have a China holly in the foreground along the brick wall. Good luck ever having this landscape planting ever seem like it is a success. The main reason I asked for an image of the whole plant is to try to determine what species/selection this actually is. That makes a huge difference in providing pruning advice. A selection like 'Dragon Lady' would need a different recommendation entirely than a selection like 'Blue Princess', since they have entirely different growth habits. A closeup of a few leaves doesn't provide the information necessary to separate these selections. I still think you have a heck of a challenge on your hands, and not one that will be solved with pruning advice. That is obviously a poorly pruned, grown, planted, and managed individual. I'd want to know a lot more before I merely tried to snip/tuck some of the current stems. I am bothering to comment on your situation because I am a KY resident and a practicing public Landscape Architect in Louisville. It is part of my job to help citizens with problems like this. A large part of my professional career was as horticulturist and landscape manager in KY prior to earning my degree in Landscape Architecture. There is often much more to consider with plant problems than the superficial conditions, and I'll assist to the extent that I'm allowed to.

look at T. o. degroots sprire ... look for single leader plants.. and try to maintain them that way ... they will outgrow many of the other arbs.. like emerald green etc ... height wise ... and i would diversify the planting .. perhaps the holly gal mentions ... i would also plant at the bottom ... why not .. i would go no more than 4 footers ... ken https://www.google.com/search?q=Thuja+occidentalis+%27DeGroot%27s+Spire%27.&source=lnms&tbm=isch&sa=X&ved=0CAgQ_AUoAmoVChMI59iW_ampxwIVB0KSCh3LTgG7&biw=870&bih=745&dpr=0.9

every leaf is a energy making machine.. to grow the roots.. to get them established for future growth ... leave them alone.. just water properly ... deeply and infrequently in fall ... though i dont know where you are.. and that might change that.. big city name ... i never pruned a new shrub for 2 years after planting.. to let it get established.. settle in.. and start growing in a normal fashion ... and then after that.. i never pruned it again.. unless it was on a world domination growth.. and then i would consider what need be done ... injury would require some pruning .... now.. go buy more plants.. so you can properly ignore this one.. lol ... ken https://sites.google.com/site/tnarboretum/Home/planting-a-tree-or-shrub

So, the Green Tower Boxwood seems like the best option. With them being slow growing, it sounds like I should hold out for 15 gallon sizes even if that means I have to wait until next spring for them to be stocked or I may be waiting many more years for them to grow large enough to be useful above the fence line. Can they be pruned into a tree-like shape with a few feet of exposed trunk so they expend their energy into growing their foliage faster higher up where they provide privacy as opposed to lower where the fence is already providing privacy? Are Green Tower and Green Pillar Boxwood the same thing?