@Boudreaux
Range Extenders are not going to be an option for you. Also because the distance is more than 328 feet, digging a conduit and running an Ethernet cable from the house to the barn is not feasible either.
You best option is to use outdoor APs like the EAP225-Outdoor or the CPE210.
EAP225-Outdoor will all dual-band communication and cover the area between the barn and home as well. though you may need two or three of these to make the distance. You can AI Mesh the EAPs to create a single seamless network
the CPE210 would be 2.4GHZ only. You would need 2 units. 1 in AP mode connected at the house and the other in Client mode connected at the barn. You would need to be line of sight and also an indoor AP for the client side to provide a signal in the barn.
For either product, support.smb@tp-link.com can answer all questions related to these business class products