New game 74 is now available.
Round 1: N T D U E N O E N
I had TUNED and... UNTENDED. Unfortunately I did not pick up the extra D until well after I would have declared that answer, so it's an invalid result for me. I did notice that if that last vowel had been an I then INNUENDO would have been available, and after time I found the seven of UNNOTED (which correctly guessing that UNTONED would not be listed).
The other seven is TENONED (TENON: "to shape so as to fit into a mortice", amongst other similar meanings); END NOTE is listed as two words only.
The sixes are TENDON, UNDONE, DENOTE, DETUNE, and TUNNED (TUN as a verb: "to put into or store in a tun or tuns"; TUN as a noun is "a large cask for holding liquids, etc., especially wine, ale, or beer").
My selection: [invalid -- UNTENDED]
Round 2: L I T D I T A H S
I had ADIT, ADITS, and DISTAL ("situated away from the point of origin or attachment, as of a limb or bone"). I also saw DISTIL but erroneously thought the spelling would only be DISTILL; later on I realised that DISTIL was fine, but not within time. After time I noted HALTS as another five, but did not see anything longer.
There is a probable seven here; LITHIA is "a white oxide of lithium [...]", so LITHIAS could be a seven. Aside from LITHIA, the other sixes are LATISH / LATHIS (LATHI: "Indian English a heavy pole or stick used as a club in India, especially by police") / TAHILS (TAHIL: "a unit of weight used in Malaysia, equal to one sixteenth of a catty"), TILTHS (TILTH: "tilled land"), and HALIDS (HALID being a variant spelling of HALIDE: "a compound, usually of two elements only, one of which is a halogen").
My selection: DISTAL
Round 3: Target 147 from 75 25 4 9 7 4
The standard method looks plausible, but the factor of 7 is hard to go past and my first solution was 147 = 7*(25 - 4). Using the standard method turned out to be a bit more difficult than I imagined, but I got there with 147 = 9*25 - 75 - (7 - 4).
My selection: 147 = 7*(25 - 4)
Round 4: R P I G A F C A T
I had GRIP, PAIR, CRAFT, amused myself by spotting AFRICA in there (it requires the capital letter, as expected; interestingly, though, AFRICAN has a lowercase sense as a colloquial term for a cigarette), and then CAPITA. I was thinking of the phrase PER CAPITA and hoping that it also had a stand-alone sense; fortunately it does, as the plural of CAPUT ("any head or headlike expansion on a structure, as on a bone").
The other sixes are TRAGIC and AGARIC ("an agaricaceous fungus", apparently). But there is a seven after all, ably found by Sam in the comments: PARFAIT ("a dessert, served in a tall glass, made from layers of ice-cream, fruit, jelly, syrup, nuts, etc."). Nice one, Sam!
My selection: CAPITA
Round 5: R M R E O M R E P
I had MORE, ERROR, and ROMPER. Just a bit too late I saw EMPEROR at last, which was doubly unfortunate as ROMPER is not valid. (ROMPER SUIT is listed, with ROMPERS given as a synonymous term, but no usage of ROMPER on its own. Bother.)
So the best to be done after EMPEROR are fives, with the others being MOPER / PROEM ("an introductory discourse"), REPRO (colloquial for "a reproduction"), ORMER (a type of abalone), and EMMER (a form of wheat).
There's an interesting situation here with MERE; it's an adjective that is listed as having an associated superlative form (MEREST) but not a comparative form, so MERER is not valid.
My selection: [invalid -- ROMPER]
Round 6: Target 408 from 6 4 7 3 2 8
The factor of 8 stands out, and the cofactor is 51. I started with 408 = (7*6 + 4 + 3 + 2)*8 and then saved a number with 408 = (7 + 6 + 4)*3*8. A little more playing around got me to the idea of 420 - 12, and the solution 408 = 6*7*(8 + 2) - 4*3.
My selection: 408 = (7*6 + 4 + 3 + 2)*8
Round 7: C C U E S S A O G
I had CUES and CAUSES / SAUCES. That was all I could get, rounding out what was a pretty unsuccessful day for me on the letters.
The sevens are ACCUSES, GASEOUS, and CASEOUS ("of or like cheese").
My selection: CAUSES
Round 8: Target 268 from 25 75 7 8 3 2
The standard method is clearly tempting as the offset of 7 is already present, and it did not take long to find 268 = 8*25 + 75 - 7. The target also factors as 4*67, leading to the solution 268 = (7 - 3)*(75 - 8).
My selection: 268 = 8*25 + 75 - 7
Round 9: SCOUR TOMB
The presence of the -OMB- fragment in the clue might help lead to the answer of COMBUSTOR. I wasn't certain about it, but it seemed too good not to be true. It is "the combustion chamber, fuel injection system, and igniter in a jet engine or ramjet".
My selection: COMBUSTOR (19.8s)