Hi Nimble. That screw holds the dust cover stop to the bottom of the cover. If it is loose then sure, tighten it. But my guess is the spring is loose or bent/cracked/broken or has just lost its tension. Unlike modern repros it is a flat spring that is screwed into the receiver (so you don't have to worry about a coil spring and ball bearing flying away like an Uberti. ). Removing the top screw will let you remove the dust cover to inspect that leaf spring. I am not personally familiar with originals, but got all that from Arthur Pirkle's book Winchester Lever Action Repeating Firearms, Vol. 1, 1866, 1873 & 1876. It is not a repair manual, don't actually know of one other than maybe David Chicoine's but those are hard to find. If you have an original you NEED the Pirkle book, and it is really cheap. I just googled it and first used one I saw was $11 shipped. Does your dust cover have the "thumbprint"?
This past year I put a 76' back together, Abilene is correct regarding the spring. Here are some places to find parts for the 76', some parts are original some are reproductions. The 73' and 76' share many parts and the dust cover spring is one of those shared parts. Have fun with the 76'! What caliber is it? Mine is 45-60, I shot it this past fall in two matches that had a Tom Horn category at their annuals.
In regards to a repair manual, I'm not sure if you'll find one. It's essentially a large 73'. Several parts are interchangeable between the 73' and 76'. Arthur Pirkle's book "The Models of 1866, 1873 & 1876" and "The Winchester Book" are helpful, in regards to the correct variations between models, but not so much as repairing the rifle.
Mine is also a 45-60 and Smokedawg who I purchased it from is sending me the components to get loaded. Been thinking to seriously get it restored by Turnbull, this and an 1887 Winchester shotgun are the oldest in my collection and I would really like to see the 1876 restored. Just have to find a 1895 and my Winchester collection will be complete lever wise with originals and replicas. I have a Navy Arms 1860, but the rest are original Winchesters or in the case of my 1866 & 1873, Moriku replicas.
If you're truly going to send the 76' to Turnbull, let them take care of missing parts. I'm certain they have their sources or stockpile. I had been considering it with mine, but I've decided to leave it has it is for now.
FURNACES: Your model number may include a series of numbers or letters, but the manuals usually cover all models that begin with that series (i.e. G8T08012UH11A) and is generally located on a sticker, on an inside wall of your furnace or on the access doors.
HUMIDIFIERS: Some models have labels which indicate the model number, while others do not. If not, refer to your installation manual cover, or visit our Humidifiers page to match your model.
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