Diaphragm pumps by nature usually do not produce deep vacuum. Most of the ones I see only produce 25" Hg at sea level. Many rotary vane vacuum pumps will produce significantly higher vacuums, usually in the 29" Hg range. The difference, from direct personal experience, in stabilizing with 25" Hg vs. 28+" Hg is quite significant. If I run my pump and control the vacuum to only reach 25" Hg, the bubbles quickly stop coming out of the wood. If I then go on up to 28" Hg, it seriously starts pulling air out of the blanks to the point it will foam over if not gradually increased.
Rotary vane pumps are frequently rated in microns and the lower the better. For example, 25.98" Hg is equal to 100,000 microns and represents an 87% vacuum. My rotary vane pump is rated at 25 microns which equates to approximately 29.9165" Hg or 99.995% vacuum. ( A perfect vacuum or absolute vacuum is 29.92" Hg and can not physically be exceeded, contrary to what you see occasionally where folks claim to be getting 31" Hg!) Of course this rating is assuming sea level and is in a perfect world with no leaks, etc. For every 1,000' above sea level, you loose 1" Hg of vacuum due to less atmospheric pressure.
The pump you have will not gain any more vacuum by hooking the 2 sections together, it will just do it faster and that is if you do as the picture above shows. If you just hook one to the other in series, it will not even do it faster since one pump will just be pumping the exhaust from the other side.
Hope that helps some and does not confuse things too much!