How do I minimize withdrawal fees from exchanges with Lightning network?

Hi everyone. I've already posted this post on r/Bitcoin sub, but it got removed for some reason. So I am posting it here in hope to get good advice.

Recently, due to high on-chain fees plus exchange withdrawal fees on top of that, I have been looking into alternative methods of withdrawing my monthly DCA BTC from exchanges.

I usually DCA somewhat around $100-200 a month. I always buy it on Binance and withdraw the very same moment to my hardware wallet. The actual process is a bit more complicated for me, as I have to use my local exchange to get some crypto. It's terrible for BTC, as its fee is 0.001 BTC per withdrawal, so I always use XLM to move my funds to Binance.

Lately, withdrawing from Binance costs around $7-17, which is total bunkers. Obviously, I don’t want to pay 10% of my deposit. It’s too much for me. It's not like I am moving millions of crypto here to neglect puny 20 bucks.

After some investigation, turns out I have a few ways to minimize my fees:

1. Accumulate BTC on the exchange (Binance) and then move it to my wallet after about 6 months when fees don’t look too scary for a bigger withdrawal.
2. Withdraw to a side-chain like BSC, Stellar or whatever. Not the biggest fan of this approach, but I am just listing my possibilities here. Maybe even buy BTC on Stellar and keep it there. It has means to withdraw BTC via anchors that provide Lightning deposit/withdrawals.
3. Withdraw to Lightning network. Accumulate it there and then move to my hardware wallet.

I am leaning more towards 3rd approach. Still considering the 1st one, but much less, as you know there is a big issue going on with Binance currently. Hell, I even start thinking that 2nd approach with Stellar doesn't sound that bad after all.

If I choose Lightning approach, will it actually save me some BTC on the fees? I mean, it is obviously dirty cheap to withdraw from exchanges, but the problem starts with all this channel juggling.

For example, I want to use a Phoenix wallet. To receive my BTC, I need inbound liquidity. So Phoenix will open a channel for a fee (on-chain transaction) for me. Then the next month I buy and withdraw BTC again, a new channel has to be opened or rebalanced as there is not enough liquidity on an older channel. And finally, when I move coins from Lightning wallet to my hardware wallet, I have to pay on-chain fees again.

Probably it will save me some sats as I don’t pay premium to exchange and I can set my own fees when I move Bitcoin back on-chain. But is it worth the hassle?

Maybe I should set up my own Lightning node and open channels directly with Binance if that is possible? But why would Binance lock its liquidity with me? Sorry I might sound really stupid.

I feel like I am trying to use Lightning the way it is not supposed to be used. If my understanding correct, it should be used for spending your BTC and receiving payments quickly with places you usually interact a lot.

Would appreciate any advice or insight. Please enlighten me on this matter, as I am struggling a bit with Lightning network even though I've been for quite some time in crypto space.

TLDR

Trying to find the best way to minimize exchange withdrawal fees for BTC. Any advice is appreciated: side-chains, Lightning, keeping on exchange, whatever. Feel free to share your opinion and experience.