Get some Hargrove radiant heat logs for vented fireplace. They throw off much more heat than a standard gas log set. We originally had gas logs in our vented fireplace and there was almost no heat. Then I bought the Hargrove radiant heat logs about 15 years ago. Our family room which is 13 x 22 is heated very well by this log set. It's not the same as burning wood, but way better than most gas log sets in a vented scenario. And way cheaper than the inserts. More on reddit.com

You don't need an insert in your existing fireplace for ventless logs. However, there is no real effective way to use a blower with gas logs like this. They give off okay radiant heat which is why they aren't intended for heat like a direct vent gas insert is. More on reddit.com

I am guessing that first measurement is your width? My Suggestion is the Majestic Ruby or Trilliant. They both offer a good all in package out the box while also having a good traditional or contemporary design. They both are very easy to use and provide full flame height and blower speed control. You can even upgrade them to be used with your smart phone through your home wifi if desired. Ruby Trilliant Pretty much any gas insert you get that comes from a reputable brand is going to be electronic ignition and comes with a blower. So it will require power. If you have an outlet close to your fireplace already, there is no need to bring any additional power unless you want a power receptacle inside the firebox to hide your power cord for aesthetic reasons. Both of these units allow for your mantel to sit above it along with a TV above that. I personally do not find having a TV above your fireplace takes away any focal point if the function of your room is to have entertainment. If you and your family watches TV and movies there or your friends come over to watch sports, then that is already part of the main focal point of the movie. More on reddit.com

I was going to say no since ventless logs push their heat out into the room anyways, but looking up your firebox it looks like they do make a blower kit that might work with, though it could just be for a variant. Your best bet would be to get in touch with a local gas log/fireplace company that could tell you for sure if it's possible and what would be involved. More on reddit.com