I will offer my chain of reasoning:
1. Oswald requested to go to the Paine home on Thursday, which was unusual, because he needed his rifle for use on Friday.
2. When Frazier asked why, Oswald answered curtain rods because he knew he would have a long, stiff, possibly metallic-sounding package the next morning.
3. Oswald said nothing to Marina or Ruth about curtain rods because (1) he didn't want to be burdened with curtain rods as well as his rifle and (2) he wanted to be alone in the garage on his own terms and not with either woman observing him.
4. Ruth and Marina said that Oswald had said nothing about curtain rods; there was no reason for them to lie, and it would have been odd for Oswald not to offer this explanation if it were true.
5. Marina said the disassembled rifle was wrapped in a blanket in the Paine garage. There was no reason for her to lie, especially since she thought it was still there.
6. Michael Paine testified about the contents of the blanket, his testimony being a near-perfect match for the disassembled rifle and his estimate of the length being 37".
7. The curtain rod story makes little sense for a frugal character like Oswald, who was merely renting his tiny room. The only curtain rods in the Paine garage belonged to Ruth, so Oswald would either have had to steal them or lower himself to asking Ruth if he could have them; this is unlikely for the proud Oswald, especially since curtain rods cost only $1 or less.
8. Frazier told Randle about the curtain rod story on Thursday evening, just as Randle said.
9. Randle saw Oswald carrying the package in one hand with the other end nearly touching the ground and observed that the package seemed bulky and heavy, which would fit the disassembled rifle better than curtain rods or a lunch; there was no reason for her to lie about this.
10. Oswald told Frazier the package contained curtain rods and that he had not brought his lunch; there was no reason for Frazier to lie about this.
11. At the TSBD, Oswald walked rapidly ahead of Frazier with the package close against his side, just as Frazier said, because he wanted the package to be as inconspicuous as possible.
12. Even if the contents of the package were discovered, Oswald would have had the convenient explanation that other rifles had recently been brought into the building and he just wanted to show his; the project was not as risky as it might seem.
13. A rifle that was traceable to Oswald and that had been stored in the Paine garage was found on the sixth floor where Oswald had been working.
14. Oswald was not observed with anything but a Coke by Mrs. Reid and was not observed with anything in his hands on the bus, by Whaley or by Earlene Roberts.
15. No curtain rods were found in the TSBD or Oswald's room.
16. Oswald denied the curtain rod story during interrogation, making Frazier and Randle appear to be liars because (1) he knew there were no curtain rods and (2) a package of curtain rods would have sounded suspiciously like a disassembled rifle; better to just deny the whole thing. If he actually had brought curtain rods, this would have been an excellent alibi.
17. Oswald said he had brought a lunch, again making Frazier appear to be a liar; when Holmes asked if it had possibly been brought in a large grocery sack, Oswald quickly agreed with this highly improbable suggestion because he knew he had been carrying a large package.
18. The likelihood of someone carrying a sandwich and apple in a large grocery sack is close to nil; Oswald offered no explanation for where the sack might be.
Based on the above, the conclusion that Oswald was carrying the disassembled rifle seems to have a very high degree of plausibility. Everything fits together nicely.
The flies in the ointment are the length estimates of Frazier and Randle.
1. Randle originally estimated the length at three feet.
2. The discrepancy arose when Frazier and Randle were questioned at the car by Odum.
a. Did Frazier, who had initially been a suspect, perhaps have a motive for suggesting the package seemed too small to hold a rifle?
b. Did Randle perhaps have a motive not to make her brother look like a fool, whereupon she settled on a length of 27"?
3. At the Warren Commission, Randle was pretty well locked into her prior story since it had involved recreating the package, but at the WC the length did increase to 28.5."
4. Although Randle impressively stuck by her estimate, we can reasonably question how much attention either she or Frazier would have paid under the circumstances (i.e., the importance of Oswald and the package being completely unknown before the assassination). This applies as well to Frazier's observation of the way Oswald supposedly carried the package into the TSBD; he was some 50 feet ahead of Frazier, and Frazier acknowledged at the mock trial that the end might have been protruding.
Hence, I see Frazier's and Randle's estimates as being problematical but explainable and not sufficient to dent the high plausibility of the disassembled rifle explanation.
I would invite those who disagree to take us through a similar chain of reasoning for curtain rods, a sandwich and an apple, or whatever else the package might have held.