chevron is a favorite that can also be done ith. this is turning out very nicely Sue. I am thinking the 9 patch as well, flying geese is another one, I have seen that done on Missouri Star Quilt Co. I am sure there are many more too ~hugs~

You can use almost any line block you like for quilt as you go. Have you thought about using embroidery or applique? You can hoop your backing, batting, and top fabric then embroider or applique on the block . That will serve as the quilting for the block. They are quick to do and you can double the amount of blocks you have then set them with one line block and one embroidered. Tried to upload a pic of one I
did that with but can't do it with my laptop.

Very nice blocks...I am not sure any can be used as strip and flip...usually flip and strip is done with a full backing and batting and the top is then stripped and flipped over both. There are a few methods to join ITH blocks, but most allow a bit more around the perimeter to work with...some join with a sashing between the blocks and some join with the sashing built into the embroidered block...Queen of Stitching has a couple of methods to join ITH blocks...so does Jenny Hasking (the Jenny Join method is done with decorative stitching over top of the "seam" to join the blocks...Here is a link for Queen of Stitching...they have several videos...and one link from Projects to a table runner I did with the Jenny Join method....

https://www.queenofstitching.com/

I use the quilt as you go method all the time, especially when I embroider
blocks to go into a quilt or wallhanging. I use the method from Hoop sisters. Any block can be used this way. You can download a Pdf tutorial free from their site. I often use the same fabric for the strips as the back
of the quilt, or you can use a contrast and it will be a double sided quilt.
Hope this will help you. http://www.hoopsisters.com/freebies/

Your quilt is very pretty, sorry unable to help you. Am interested to read all the comments for my memory bank. Sandra.

Just to clarify. My blocks are made in the hoop. First I hoop thin fabric (old sheeting.) Then I add a layer of wadding and build up the block from my digitised design. Finally I add fabric beneath the hoop and a square outline to hold it all together and act as a stitching line for joining. When I've done enough squares!

I like much! Lillian

Okay...I was thinking you were looking for a block joining method....silly me! As far as blocks that can be made ITH from the "flip and strip" method...Lots of paper pieced blocks can be adapted and digitized to be stitched ITH...

Still hoping for more suggestions........

Here are some sites that you're sure to see some things you like. At Carol Doak, you need to click on free patterns. Quilter's Cache is the greatest quilt site ever.
Jo

Here is an archived link to Threads That Bind Us, which recently closed. You can see many of her designs by clicking on the pictures. There is at least 1 free design to download.
https://web.archive.org/web/20150216021015/http://www.secretsof.com/content/2411
Here is a chart to enlarge/reduce blocks that may be helpful.
https://web.archive.org/web/20141110025002/http://www.pieceinthehoop.com/shop/index.php?main_page=page&id=11
Here are designs from SewAZ.
http://www.sewazdesigns.com/designs.aspx?sr=ith%20quilt%20block
These are from Cassandra.
http://www.cassandrasembroidery.com/Quilting%20Redwork%20Sets/QuiltRedworkSetsALL.html
Lindeegembroidery:http://lindeegembroidery.com/shop/index.php?main_page=product_info&cPath=1_13&products_id=72&zenid=0hjbba38mdcbe1j1rlfcsm4iv4
Sweetpea:http://swpea.com/collections/quilts-and-quilting-in-the-hoop
Amazing Designs:http://amazingdesigns.com/in-the-hoop-quilt-blocks

Kenny Kreations also has some blocks.
https://www.kennykreations.com/categories/114/piece-in-the-hoop/
Here are 36 Crazy Quilt designs from Anita Goodesign that are free to download. Scroll down to "Crazy Quilt Designs and Instructions".
http://www.anitagoodesignonline.com/downloads/

Sue-how about the Dresden Plate--top plain fabric as foundation piece and then place the first 'blade' continue on ITH with each 'blade' stitched on previous, right sides facing then flip until all 'blades around. Finally top with a square piece of material you have digitized into a circle, trim and satin stitch the circle, then continue on with your layer of batting and backing?????

how about a rail fence? Half Square triangles, strip piece on an angle (shown below) snowball block would be another easy one ~hugs~

These are excellent. I love the flying geese and could see a good sized quilt made with it.