How to deal with long chip lead times in small company
Overhauling the product to avoid lead times is absolutely the wrong approach. You will not win this battle, stuff will go out of stock, because life happens. You could very well switch to a new chip only to find out that in six months that part has gone out of stock, and the original part is back in stock. In the meantime, you will have burned a bunch of NRE designing and qualifying the new component.

The only way to guarantee that you have parts when you need them is to order parts early and hold stock either yourself or in a specialty warehouse.

I would only design a part out for supply issues if there was a persistent issue with getting parts (ie: it happened more than once or twice) and/or the vendor's delivery estimates were longer than they estimated. If TI tells me that a part's out of stock and it'll take 16 weeks for them to cut new wafers, well, that's life. As long as they actually deliver in 16 weeks I can't well complain, can I?

The smart, prudent thing is to forecast your production volumes well in advance. If you know you'll be trying to sell 10k units in Q2 2018, then you should be queuing up your contract manufacturer now in order to get all the purchase orders in place so you can build the units on-time.

In tandem with this, you can rely on credit from your contract manufacturer, especially if you have firm orders in the pipeline - so if you can't afford the parts now, your CM can absorb the cost and let you pay later. You might also be able to negotiate a deal with your contract manufacturer where they buy and store the parts and then sell them to you when you make a production run, especially if it's something that multiple customers use like passives.

At the end of the day, making hardware means spending money well in advance of selling a product. The Bolt blog has a great article on the hardware startup valley of death: it happens when you start selling product, because there's a long lead time between ordering a production run, executing on that production run, and sell-through in retail.