$1000 would be hard but a smokeless 45 is easily doable for under $1500. One of the newer higher BC bullets for sabotless smokeless will help a little too.
When the Savage MLII could be found for around $500-600 all you needed was a 45cal barrel and a sizing die. Mine has no problem sending a 275gr bullet down range at 2700fps or more. Those barrels still cost from around $400-500 but a MLII now is really pricey.
The least expensive way atm is converting a break action 45/70 to a smokeless 45cal ML. They will easily send a 200gr sabotted bullet down range at over 2500fps and sabotless about the same speed.
Recoil can get pretty brisk on these lighter weight break action conversions and you would be working with a OEM barrel. In most cases though they would be a 300 yard capable rifle. 200 yards pretty easily.
CVA Apex 45/70 if you can still find one ....about $550
Breach plug and labor....around $200
Sizing die.....around $140
CVA Scout V2 45/70...around $350 but the barrel is only 22"
CVA Hunter 45/70 25" barrel.....around $250 or slightly less.
Here is a video of this type of conversion. The LRMP conversion cost more, about $300. 60gr of 4198 and a 275gr bullet will give you about 2500fps.