Hi TX635,
Welcome and good luck with your project. The contract rifle kit from TOW looks like it will make a very unbalanced and barrel heavy gun. However, that is historically correct because most contract rifles were heavy, clumsy, and many were poorly made. What rifles L&C carried is unknown and the papers arguing for contract rifles and those for a Harper's Ferry prototype short rifles are based on weak circumstantial evidence. There is an original short rifle styled like the Harper's Ferry model 1803 rifle with number 15 that is purported to be one of those carried by L&C. The Rifle Shoppe even sells a parts set for it. Still there is no widely accepted "smoking gun". Regardless, if you want a nice handling and historically consistent rifle for the late 18th and early 19th centuries, there are better choices. Kits by Jim Kibler would be the easiest to build, particularly if you have limited work space in an apartment. They are hands down the best produced kits you can buy and as close to "snap together" as you will find. The end results are fine guns, shaped correctly, and very shootable. However, if you want to do more hands on work to acquire skills, kits by Jim Chambers are a good option. They offer a wider variety of guns that are historically consistent and include excellent quality components. TOW kits can be pretty good but I would urge you to get one that fits a swamped barrel not a straight one. The best book, IMO, for step by step instruction is Dixon's "The Art of Building the Pennsylvania Rifle" . Peter Alexander's book is more comprehensive but it was produced from a collection of articles he published individually so it is disjointed as a step by step guide. Be very careful using videos on You Tube. Jim Kibler's and Bill Raby's videos are good but there are many that are absolutely terrible by folks who don't know what they are doing. As with every thing on the internet, you have to glean kernels from a lot of chaff. One of the biggest problems for new builders is most really don't know what a traditional flintlock long rifle looks like. They miss how the wrist and lock panels were shaped, the slimness of the fore stock, and many other details despite looking at photos. The advantage of Kibler's kits is when you are done, you will have an excellent model for what a real long rifle looks like designed by a master builder. The trade off is that 99% of the work is done by Jim's CNC assisted machinery and you cannot change much to suit your tastes and you won't learn many inletting and shaping skills. Less finished kits like Chambers will require you learn more skills and allows more individuality but the trade off is you can also have greater risk of mistakes and getting the styling and details wrong.
Visit this link to see a Kibler kit assembled by a master builder and you can see what a superb design it is.
https://www.muzzleloadingforum.com/threads/kibler-colonial-kit-assembled.132856/page-2Keep in mind that Dave's version has engraving and carving superior to what is found on original long rifles.
dave